Daily Papers

Conversational shopping agents represent a critical consumer-facing application of Large Language Model (LLM)-powered agents, yet how to effectively apply post-training Reinforcement Learning (RL) to optimize such agents remains underexplored. This work investigates RL-based optimization for shopping agents in real-world scenarios, where agents must simultaneously satisfy multiple interdependent objectives spanning objective metrics (product correctness), subjective qualities (persuasiveness), outcome rewards (final response quality), and process rewards (tool efficiency). We present a complete methodology to address this challenge. Specifically, we first construct SmartShopBench, a benchmark that captures diverse shopping intents with a hierarchical evaluation that decomposes complex quality requirements into measurable levels. Building on this evaluation framework, we design Hierarchical Reward Modeling (HRM) to structure mixed reward types through conditional gating that reflects their logical dependencies. To enable efficient training, we further propose Dynamic Contrastive Policy Optimization (DCPO), which balances response quality with operational efficiency through dynamic trajectory selection based on reward and reasoning length. Extensive experiments demonstrate that our RL-trained agent, namely ChatShopBuddy, consistently outperforms larger models relying on generic reasoning, achieving superior stability rather than merely higher peaks. Our work provides valuable guidance for applying RL to real-world conversational agents.

Agentic reinforcement learning has enabled large language models to perform complex multi-turn planning and tool use. However, learning in long-horizon settings remains challenging due to sparse, trajectory-level outcome rewards. While prior tree-based methods attempt to mitigate this issue, they often suffer from high variance and computational inefficiency. Through empirical analysis of search agents, We identify a common pattern: performance diverges mainly due to decisions near the tail. Motivated by this observation, we propose Branching Relative Policy Optimization (BranPO), a value-free method that provides step-level contrastive supervision without dense rewards. BranPO truncates trajectories near the tail and resamples alternative continuations to construct contrastive suffixes over shared prefixes, reducing credit ambiguity in long-horizon rollouts. To further boost efficiency and stabilize training, we introduce difficulty-aware branch sampling to adapt branching frequency across tasks, and redundant step masking to suppress uninformative actions. Extensive experiments on various question answering benchmarks demonstrate that BranPO consistently outperforms strong baselines, achieving significant accuracy gains on long-horizon tasks without increasing the overall training budget. Our code is available at https://github.com/YubaoZhao/BranPO{code}.

Alignment in large language models (LLMs) is still largely static: after training, the policy is frozen. DPO, GRPO methods typically imprint one behavior into the weights, leaving little runtime control beyond prompt hacks or expensive re-alignment. We introduce ECLIPTICA, which treats alignment as instruction-driven and runtime-controllable: natural-language alignment instructions act as an explicit behavioral contract (stance, refusal boundary, verbosity) that modulates behavior on the fly under evolving safety requirements, user roles, and governance constraints. We introduce CITA (Contrastive Instruction-Tuned Alignment), combining SFT with contrastive preference optimization under an explicit geometric anchor to a reference model. This yields a stable Riemannian chart and keeps instruction updates within a shared neighborhood, so regimes stay nearby and traversable for reliable switching. To isolate policy switching from ordinary instruction following, we release the ECLIPTICA benchmark: 3000 controlled cases (300 prompts x 10 instruction types) where the user request is fixed and only the alignment instruction changes. On Llama-3.1-8B across five suites (ECLIPTICA, TruthfulQA, Conditional Safety, Length Control, LITMUS), CITA reaches 86.7% instruction-alignment efficiency, beating DPO (56.1%), GRPO (36.1%), and PPO (20.4%).

In view of its power in extracting feature representation, contrastive self-supervised learning has been successfully integrated into the practice of (deep) reinforcement learning (RL), leading to efficient policy learning in various applications. Despite its tremendous empirical successes, the understanding of contrastive learning for RL remains elusive. To narrow such a gap, we study how RL can be empowered by contrastive learning in a class of Markov decision processes (MDPs) and Markov games (MGs) with low-rank transitions. For both models, we propose to extract the correct feature representations of the low-rank model by minimizing a contrastive loss. Moreover, under the online setting, we propose novel upper confidence bound (UCB)-type algorithms that incorporate such a contrastive loss with online RL algorithms for MDPs or MGs. We further theoretically prove that our algorithm recovers the true representations and simultaneously achieves sample efficiency in learning the optimal policy and Nash equilibrium in MDPs and MGs. We also provide empirical studies to demonstrate the efficacy of the UCB-based contrastive learning method for RL. To the best of our knowledge, we provide the first provably efficient online RL algorithm that incorporates contrastive learning for representation learning. Our codes are available at https://github.com/Baichenjia/Contrastive-UCB.

Reinforcement Learning (RL) has been used to finetune Large Language Models (LLMs) using a reward model trained from preference data, to better align with human judgment. The recently introduced direct alignment methods, which are often simpler, more stable, and computationally lighter, can more directly achieve this. However, these approaches cannot optimize arbitrary rewards, and the preference-based ones are not the only rewards of interest for LLMs (eg., unit tests for code generation or textual entailment for summarization, among others). RL-finetuning is usually done with a variation of policy gradient, which calls for on-policy or near-on-policy samples, requiring costly generations. We introduce Contrastive Policy Gradient, or CoPG, a simple and mathematically principled new RL algorithm that can estimate the optimal policy even from off-policy data. It can be seen as an off-policy policy gradient approach that does not rely on important sampling techniques and highlights the importance of using (the right) state baseline. We show this approach to generalize the direct alignment method IPO (identity preference optimization) and classic policy gradient. We experiment with the proposed CoPG on a toy bandit problem to illustrate its properties, as well as for finetuning LLMs on a summarization task, using a learned reward function considered as ground truth for the purpose of the experiments.

Reinforcement learning has been widely applied to enhance the reasoning capabilities of large language models. Extending the inference limits of smaller models has become a prominent research focus. However, algorithms such as Group Relative Policy Optimization (GRPO) suffer from a clear drawback: the upper bound of a model's rollout responses is entirely determined by the model itself, preventing the acquisition of knowledge from samples that are either all incorrect or all correct. In this paper, we introduce Group Contrastive Policy Optimization (GCPO), a method that incorporates external standard reference answers. When the model cannot solve a problem, the reference answer supplies the correct response, steering the model toward an unequivocally accurate update direction. This approach offers two main advantages: (1) it improves training efficiency by fully utilizing every sample; (2) it enables the model to emulate the problem solving strategy of the reference answer during training, thereby enhancing generalization in reasoning. GCPO achieves outstanding results across multiple benchmark datasets, yielding substantial improvements over the baseline model. Our code is available at: https://github.com/AchoWu/GCPO.

Contrastive reinforcement learning (CRL) learns goal-conditioned Q-values through a contrastive objective over state-action and goal representations, removing the need for hand-crafted reward functions. Despite impressive success in achieving viable self-supervised learning in RL, all existing CRL algorithms rely on off-policy optimisation and are mostly constrained to continuous action spaces, with little research invested in discrete environments. This leaves CRL disconnected from widely used and effective, modern on-policy training pipelines adopted across both single-agent and multi-agent RL in continuous and discrete environments. To establish a first connection, we introduce Contrastive Proximal Policy Optimisation (CPPO). CPPO is an on-policy contrastive RL algorithm that derives policy advantages directly from contrastive Q-values and optimises them via the standard PPO objective, without requiring a reward function or a replay buffer. We evaluate CPPO across continuous and discrete, single-agent and cooperative multi-agent tasks. Whilst the existence of an on-policy approach is inherently useful, we observe that CPPO not only significantly outperforms the previous CRL baselines in 14 out of 18 tasks, but also matches or exceeds PPO's performance, which uses hand-crafted dense rewards, in 12 out of the 18 tasks tested.

Group Relative Policy Optimization (GRPO) is a prominent reinforcement learning algorithm for post-training Large Language Models (LLMs). It is commonly believed that GRPO necessitates a large group size to ensure stable training via precise statistical estimation, which incurs substantial computational overhead. In this work, we challenge this assumption by reframing GRPO as a form of contrastive learning, which reveals a fundamental connection to Direct Preference Optimization (DPO). Motivated by DPO's empirical success, we investigate the minimal two-rollout case (2-GRPO), a configuration previously deemed infeasible. We provide a rigorous theoretical analysis to validate 2-GRPO and demonstrate empirically that it achieves performance on par with 16-GRPO, despite using only 1/8 of the rollouts and reducing training time by over 70%.

Prevailing methods for training Large Language Models (LLMs) as text encoders rely on contrastive losses that treat the model as a black box function, discarding its generative and reasoning capabilities in favor of static embeddings. We introduce GRACE (Generative Representation Learning via Contrastive Policy Optimization), a novel framework that reimagines contrastive signals not as losses to be minimized, but as rewards that guide a generative policy. In GRACE, the LLM acts as a policy that produces explicit, human-interpretable rationales--structured natural language explanations of its semantic understanding. These rationales are then encoded into high-quality embeddings via mean pooling. Using policy gradient optimization, we train the model with a multi-component reward function that maximizes similarity between query positive pairs and minimizes similarity with negatives. This transforms the LLM from an opaque encoder into an interpretable agent whose reasoning process is transparent and inspectable. On MTEB benchmark, GRACE yields broad cross category gains: averaged over four backbones, the supervised setting improves overall score by 11.5% over base models, and the unsupervised variant adds 6.9%, while preserving general capabilities. This work treats contrastive objectives as rewards over rationales, unifying representation learning with generation to produce stronger embeddings and transparent rationales. The model, data and code are available at https://github.com/GasolSun36/GRACE.

Markov Decision Processes (MDPs) are a formal framework for modeling and solving sequential decision-making problems. In finite-time horizons such problems are relevant for instance for optimal stopping or specific supply chain problems, but also in the training of large language models. In contrast to infinite horizon MDPs optimal policies are not stationary, policies must be learned for every single epoch. In practice all parameters are often trained simultaneously, ignoring the inherent structure suggested by dynamic programming. This paper introduces a combination of dynamic programming and policy gradient called dynamic policy gradient, where the parameters are trained backwards in time. For the tabular softmax parametrisation we carry out the convergence analysis for simultaneous and dynamic policy gradient towards global optima, both in the exact and sampled gradient settings without regularisation. It turns out that the use of dynamic policy gradient training much better exploits the structure of finite-time problems which is reflected in improved convergence bounds.

Reinforcement learning has become a cornerstone technique for developing reasoning models in complex tasks, ranging from mathematical problem-solving to imaginary reasoning. The optimization of these models typically relies on policy gradient methods, whose efficacy hinges on the accurate estimation of an advantage function. However, prevailing methods typically employ static advantage estimation, a practice that leads to inefficient credit assignment by neglecting the dynamic utility of training samples over time. This limitation results in suboptimal policy updates, which in turn manifest as slower convergence rates and increased learning instability, as models fail to adapt to evolving sample utilities effectively. To address this problem, we introduce ADORA (Advantage Dynamics via Online Rollout Adaptation), a novel framework for policy optimization. ADORA dynamically adjusts the advantage function's weighting by adaptively categorizing training data into temporarily advantageous and disadvantageous samples, based on their evolving utility during online model rollouts. This tailored data differentiation strategy allows ADORA to be seamlessly integrated into existing policy optimization algorithms without significant architectural modifications, enabling the policy to prioritize learning from more informative experiences and thereby achieve more efficient policy updates. Extensive evaluations across diverse model families and varying data scales demonstrate that ADORA is a robust and efficient framework. It significantly enhances long reasoning in both geometric and mathematical tasks, consistently achieving notable performance gains without requiring sensitive hyperparameter tuning.

Reinforcement learning from human feedback (RLHF) has been extensively employed to align large language models with user intent. However, proximal policy optimization (PPO) based RLHF is occasionally unstable requiring significant hyperparameter finetuning, and computationally expensive to maximize the estimated reward during alignment. Recently, direct preference optimization (DPO) is proposed to address those challenges. However, DPO relies on contrastive responses generated from human annotator and alternative LLM, instead of the policy model, limiting the effectiveness of the RLHF. In this paper, we addresses both challenges by systematically combining rejection sampling (RS) and DPO. Our proposed method, RS-DPO, initiates with the development of a supervised fine-tuned policy model (SFT). A varied set of k responses per prompt are sampled directly from the SFT model. RS-DPO identifies pairs of contrastive samples based on their reward distribution. Finally, we apply DPO with the contrastive samples to align the model to human preference. Our experiments indicate that our proposed method effectively fine-tunes LLMs with limited resource environments, leading to improved alignment with user intent. Furthermore, it outperforms existing methods, including RS, PPO, and DPO.

Critic-free methods like GRPO reduce memory demands by estimating advantages from multiple rollouts but tend to converge slowly, as critical learning signals are diluted by an abundance of uninformative samples and tokens. To tackle this challenge, we propose the Dynamic Dual-Level Down-Sampling (D^3S) framework that prioritizes the most informative samples and tokens across groups to improve the efficient of policy optimization. D^3S operates along two levels: (1) the sample-level, which selects a subset of rollouts to maximize advantage variance (Var(A)). We theoretically proven that this selection is positively correlated with the upper bound of the policy gradient norms, yielding higher policy gradients. (2) the token-level, which prioritizes tokens with a high product of advantage magnitude and policy entropy (|A_{i,t}|times H_{i,t}), focusing updates on tokens where the policy is both uncertain and impactful. Moreover, to prevent overfitting to high-signal data, D^3S employs a dynamic down-sampling schedule inspired by curriculum learning. This schedule starts with aggressive down-sampling to accelerate early learning and gradually relaxes to promote robust generalization. Extensive experiments on Qwen2.5 and Llama3.1 demonstrate that integrating D^3S into advanced RL algorithms achieves state-of-the-art performance and generalization while requiring fewer samples and tokens across diverse reasoning benchmarks. Our code is added in the supplementary materials and will be made publicly available.

In meta reinforcement learning (meta RL), an agent seeks a Bayes-optimal policy -- the optimal policy when facing an unknown task that is sampled from some known task distribution. Previous approaches tackled this problem by inferring a belief over task parameters, using variational inference methods. Motivated by recent successes of contrastive learning approaches in RL, such as contrastive predictive coding (CPC), we investigate whether contrastive methods can be used for learning Bayes-optimal behavior. We begin by proving that representations learned by CPC are indeed sufficient for Bayes optimality. Based on this observation, we propose a simple meta RL algorithm that uses CPC in lieu of variational belief inference. Our method, ContraBAR, achieves comparable performance to state-of-the-art in domains with state-based observation and circumvents the computational toll of future observation reconstruction, enabling learning in domains with image-based observations. It can also be combined with image augmentations for domain randomization and used seamlessly in both online and offline meta RL settings.

Flow-based generative models, including diffusion models, excel at modeling continuous distributions in high-dimensional spaces. In this work, we introduce Flow Policy Optimization (FPO), a simple on-policy reinforcement learning algorithm that brings flow matching into the policy gradient framework. FPO casts policy optimization as maximizing an advantage-weighted ratio computed from the conditional flow matching loss, in a manner compatible with the popular PPO-clip framework. It sidesteps the need for exact likelihood computation while preserving the generative capabilities of flow-based models. Unlike prior approaches for diffusion-based reinforcement learning that bind training to a specific sampling method, FPO is agnostic to the choice of diffusion or flow integration at both training and inference time. We show that FPO can train diffusion-style policies from scratch in a variety of continuous control tasks. We find that flow-based models can capture multimodal action distributions and achieve higher performance than Gaussian policies, particularly in under-conditioned settings.

Despite recent progress in reinforcement learning (RL) from raw pixel data, sample inefficiency continues to present a substantial obstacle. Prior works have attempted to address this challenge by creating self-supervised auxiliary tasks, aiming to enrich the agent's learned representations with control-relevant information for future state prediction. However, these objectives are often insufficient to learn representations that can represent the optimal policy or value function, and they often consider tasks with small, abstract discrete action spaces and thus overlook the importance of action representation learning in continuous control. In this paper, we introduce TACO: Temporal Action-driven Contrastive Learning, a simple yet powerful temporal contrastive learning approach that facilitates the concurrent acquisition of latent state and action representations for agents. TACO simultaneously learns a state and an action representation by optimizing the mutual information between representations of current states paired with action sequences and representations of the corresponding future states. Theoretically, TACO can be shown to learn state and action representations that encompass sufficient information for control, thereby improving sample efficiency. For online RL, TACO achieves 40% performance boost after one million environment interaction steps on average across nine challenging visual continuous control tasks from Deepmind Control Suite. In addition, we show that TACO can also serve as a plug-and-play module adding to existing offline visual RL methods to establish the new state-of-the-art performance for offline visual RL across offline datasets with varying quality.

Group-advantage-based reinforcement learning methods, such as GRPO and DAPO, have demonstrated strong performance across diverse domains, including mathematical reasoning and text-to-image generation. However, their reliance on sample-level rewards introduces a key limitation as uniform credit assignment across all tokens fails to capture fine-grained, token-level contributions. To address this issue, we propose Guidance Contrastive Policy Optimization (GCPO), a novel algorithm that enables per-token credit assignment by contrasting model predictions under positive and negative prompts. Rather than uniformly broadcasting sample-level advantages, GCPO assigns token-level advantages proportional to the difference between these contrastive predictions, allowing more precise and informative learning signals. Empirically, we find that GCPO emphasizes semantically relevant regions such as visual areas aligned with textual prompts in text-to-image generation, and critical keywords within reasoning traces for chain-of-thought tasks. Through extensive experiments, GCPO consistently outperforms GRPO and DAPO baselines on both text-to-image generation and chain-of-thought reasoning benchmarks, demonstrating its effectiveness as a general and scalable optimization strategy for discrete policy learning.

Generalizing policies across different domains with dynamics mismatch poses a significant challenge in reinforcement learning. For example, a robot learns the policy in a simulator, but when it is deployed in the real world, the dynamics of the environment may be different. Given the source and target domain with dynamics mismatch, we consider the online dynamics adaptation problem, in which case the agent can access sufficient source domain data while online interactions with the target domain are limited. Existing research has attempted to solve the problem from the dynamics discrepancy perspective. In this work, we reveal the limitations of these methods and explore the problem from the value difference perspective via a novel insight on the value consistency across domains. Specifically, we present the Value-Guided Data Filtering (VGDF) algorithm, which selectively shares transitions from the source domain based on the proximity of paired value targets across the two domains. Empirical results on various environments with kinematic and morphology shifts demonstrate that our method achieves superior performance compared to prior approaches.

Recent advances in large language models (LLMs) have demonstrated remarkable capabilities across diverse domains, particularly in mathematical reasoning, amid which geometry problem solving remains a challenging area where auxiliary construction plays a enssential role. Existing approaches either achieve suboptimal performance or rely on massive LLMs (e.g., GPT-4o), incurring massive computational costs. We posit that reinforcement learning with verifiable reward (e.g., GRPO) offers a promising direction for training smaller models that effectively combine auxiliary construction with robust geometric reasoning. However, directly applying GRPO to geometric reasoning presents fundamental limitations due to its dependence on unconditional rewards, which leads to indiscriminate and counterproductive auxiliary constructions. To address these challenges, we propose Group Contrastive Policy Optimization (GCPO), a novel reinforcement learning framework featuring two key innovations: (1) Group Contrastive Masking, which adaptively provides positive or negative reward signals for auxiliary construction based on contextual utility, and a (2) length reward that promotes longer reasoning chains. Building on GCPO, we develop GeometryZero, a family of affordable-size geometric reasoning models that judiciously determine when to employ auxiliary construction. Our extensive empirical evaluation across popular geometric benchmarks (Geometry3K, MathVista) demonstrates that GeometryZero models consistently outperform baselines (e.g. GRPO), achieving an average improvement of 4.29% across all benchmarks.

Agents that can learn to imitate given video observation -- without direct access to state or action information are more applicable to learning in the natural world. However, formulating a reinforcement learning (RL) agent that facilitates this goal remains a significant challenge. We approach this challenge using contrastive training to learn a reward function comparing an agent's behaviour with a single demonstration. We use a Siamese recurrent neural network architecture to learn rewards in space and time between motion clips while training an RL policy to minimize this distance. Through experimentation, we also find that the inclusion of multi-task data and additional image encoding losses improve the temporal consistency of the learned rewards and, as a result, significantly improves policy learning. We demonstrate our approach on simulated humanoid, dog, and raptor agents in 2D and a quadruped and a humanoid in 3D. We show that our method outperforms current state-of-the-art techniques in these environments and can learn to imitate from a single video demonstration.

This paper studies post-training large language models (LLMs) using preference feedback from a powerful oracle to help a model iteratively improve over itself. The typical approach for post-training LLMs involves Reinforcement Learning from Human Feedback (RLHF), which traditionally separates reward learning and subsequent policy optimization. However, such a reward maximization approach is limited by the nature of "point-wise" rewards (such as Bradley-Terry model), which fails to express complex intransitive or cyclic preference relations. While advances on RLHF show reward learning and policy optimization can be merged into a single contrastive objective for stability, they yet still remain tethered to the reward maximization framework. Recently, a new wave of research sidesteps the reward maximization presumptions in favor of directly optimizing over "pair-wise" or general preferences. In this paper, we introduce Direct Nash Optimization (DNO), a provable and scalable algorithm that marries the simplicity and stability of contrastive learning with theoretical generality from optimizing general preferences. Because DNO is a batched on-policy algorithm using a regression-based objective, its implementation is straightforward and efficient. Moreover, DNO enjoys monotonic improvement across iterations that help it improve even over a strong teacher (such as GPT-4). In our experiments, a resulting 7B parameter Orca-2.5 model aligned by DNO achieves the state-of-the-art win-rate against GPT-4-Turbo of 33% on AlpacaEval 2.0 (even after controlling for response length), an absolute gain of 26% (7% to 33%) over the initializing model. It outperforms models with far more parameters, including Mistral Large, Self-Rewarding LM (70B parameters), and older versions of GPT-4.

Learning from human preference data has emerged as the dominant paradigm for fine-tuning large language models (LLMs). The two most common families of techniques -- online reinforcement learning (RL) such as Proximal Policy Optimization (PPO) and offline contrastive methods such as Direct Preference Optimization (DPO) -- were positioned as equivalent in prior work due to the fact that both have to start from the same offline preference dataset. To further expand our theoretical understanding of the similarities and differences between online and offline techniques for preference fine-tuning, we conduct a rigorous analysis through the lens of dataset coverage, a concept that captures how the training data covers the test distribution and is widely used in RL. We prove that a global coverage condition is both necessary and sufficient for offline contrastive methods to converge to the optimal policy, but a weaker partial coverage condition suffices for online RL methods. This separation provides one explanation of why online RL methods can perform better than offline methods, especially when the offline preference data is not diverse enough. Finally, motivated by our preceding theoretical observations, we derive a hybrid preference optimization (HyPO) algorithm that uses offline data for contrastive-based preference optimization and online data for KL regularization. Theoretically and empirically, we demonstrate that HyPO is more performant than its pure offline counterpart DPO, while still preserving its computation and memory efficiency.

Recent improvements in conditional generative modeling have made it possible to generate high-quality images from language descriptions alone. We investigate whether these methods can directly address the problem of sequential decision-making. We view decision-making not through the lens of reinforcement learning (RL), but rather through conditional generative modeling. To our surprise, we find that our formulation leads to policies that can outperform existing offline RL approaches across standard benchmarks. By modeling a policy as a return-conditional diffusion model, we illustrate how we may circumvent the need for dynamic programming and subsequently eliminate many of the complexities that come with traditional offline RL. We further demonstrate the advantages of modeling policies as conditional diffusion models by considering two other conditioning variables: constraints and skills. Conditioning on a single constraint or skill during training leads to behaviors at test-time that can satisfy several constraints together or demonstrate a composition of skills. Our results illustrate that conditional generative modeling is a powerful tool for decision-making.

We study offline meta-reinforcement learning, a practical reinforcement learning paradigm that learns from offline data to adapt to new tasks. The distribution of offline data is determined jointly by the behavior policy and the task. Existing offline meta-reinforcement learning algorithms cannot distinguish these factors, making task representations unstable to the change of behavior policies. To address this problem, we propose a contrastive learning framework for task representations that are robust to the distribution mismatch of behavior policies in training and test. We design a bi-level encoder structure, use mutual information maximization to formalize task representation learning, derive a contrastive learning objective, and introduce several approaches to approximate the true distribution of negative pairs. Experiments on a variety of offline meta-reinforcement learning benchmarks demonstrate the advantages of our method over prior methods, especially on the generalization to out-of-distribution behavior policies. The code is available at https://github.com/PKU-AI-Edge/CORRO.

Policy optimization methods are powerful algorithms in Reinforcement Learning (RL) for their flexibility to deal with policy parameterization and ability to handle model misspecification. However, these methods usually suffer from slow convergence rates and poor sample complexity. Hence it is important to design provably sample efficient algorithms for policy optimization. Yet, recent advances for this problems have only been successful in tabular and linear setting, whose benign structures cannot be generalized to non-linearly parameterized policies. In this paper, we address this problem by leveraging recent advances in value-based algorithms, including bounded eluder-dimension and online sensitivity sampling, to design a low-switching sample-efficient policy optimization algorithm, LPO, with general non-linear function approximation. We show that, our algorithm obtains an varepsilon-optimal policy with only O(text{poly(d)}{varepsilon^3}) samples, where varepsilon is the suboptimality gap and d is a complexity measure of the function class approximating the policy. This drastically improves previously best-known sample bound for policy optimization algorithms, O(text{poly(d)}{varepsilon^8}). Moreover, we empirically test our theory with deep neural nets to show the benefits of the theoretical inspiration.

Reinforcement Learning with Verifiable Rewards (RLVR) enhances Large Language Model (LLM) reasoning but suffers from advantage collapse on ``hard samples'' where all rollouts fail. This lack of variance eliminates crucial learning signals. For these intractable samples, simply scaling up rollout budgets offers limited gains. We introduce Joint Policy and Prompt Optimization (P^2O) to mitigate this collapse by alternating continuous policy updates with discrete prompt evolution. P^2O leverages the GEPA algorithm to discover successful reasoning prompts for intractable instances. Via context distillation, the model internalizes these prompt-induced gains directly into its parameters, removing the need for inference-time prompting. Empirically, P^2O restores critical advantage signals, significantly outperforming standard GRPO and surpassing baselines with doubled rollout budgets, ultimately yielding strong out-of-distribution generalization and an up to 9.5% performance improvement. Our findings expose the limits of standard exploration in sparse-reward environments, illuminating the potential of unifying evolutionary algorithms with reinforcement learning. This integration of discrete semantic search and continuous parameter updates establishes a self-reinforcing paradigm for autonomous LLM alignment.

We adapt the ideas underlying the success of Deep Q-Learning to the continuous action domain. We present an actor-critic, model-free algorithm based on the deterministic policy gradient that can operate over continuous action spaces. Using the same learning algorithm, network architecture and hyper-parameters, our algorithm robustly solves more than 20 simulated physics tasks, including classic problems such as cartpole swing-up, dexterous manipulation, legged locomotion and car driving. Our algorithm is able to find policies whose performance is competitive with those found by a planning algorithm with full access to the dynamics of the domain and its derivatives. We further demonstrate that for many of the tasks the algorithm can learn policies end-to-end: directly from raw pixel inputs.

Direct Preference Optimization (DPO) has emerged as a cornerstone of reinforcement learning from human feedback (RLHF) due to its simplicity and efficiency. However, existing DPO-based methods typically treat all preference pairs equally, overlooking substantial variations in data quality and learning difficulty, which leads to inefficient data utilization and suboptimal performance. To address this limitation, we propose Uni-DPO, a unified dynamic preference optimization framework that jointly considers (a) the inherent quality of preference pairs and (b) the model's evolving performance during training. By adaptively reweighting samples based on both factors, Uni-DPO enables more effective use of preference data and achieves superior performance. Extensive experiments across models and benchmarks demonstrate the effectiveness and generalization of Uni-DPO. On textual tasks, Gemma-2-9B-IT fine-tuned with Uni-DPO surpasses the leading LLM, Claude 3 Opus, by 6.7 points on Arena-Hard. On mathematical and multimodal tasks, Uni-DPO consistently outperforms baseline methods across all benchmarks, providing strong empirical evidence of its effectiveness and robustness.

Post-training paradigms for Large Language Models (LLMs), primarily Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), face a fundamental dilemma: SFT provides stability (low variance) but suffers from high fitting bias, while RL enables exploration (low bias) but grapples with high gradient variance. Existing unified optimization strategies often employ naive loss weighting, overlooking the statistical conflict between these distinct gradient signals. In this paper, we provide a rigorous theoretical analysis of this bias-variance trade-off and propose DYPO (Dynamic Policy Optimization), a unified framework designed to structurally mitigate this conflict. DYPO integrates three core components: (1) a Group Alignment Loss (GAL) that leverages intrinsic group dynamics to significantly reduce RL gradient variance; (2) a Multi-Teacher Distillation mechanism that corrects SFT fitting bias via diverse reasoning paths; and (3) a Dynamic Exploitation-Exploration Gating mechanism that adaptively arbitrates between stable SFT and exploratory RL based on reward feedback. Theoretical analysis confirms that DYPO linearly reduces fitting bias and minimizes overall variance. Extensive experiments demonstrate that DYPO significantly outperforms traditional sequential pipelines, achieving an average improvement of 4.8\% on complex reasoning benchmarks and 13.3\% on out-of-distribution tasks. Our code is publicly available at https://github.com/Tocci-Zhu/DYPO.

Preference-based reinforcement learning (PbRL) aligns a robot behavior with human preferences via a reward function learned from binary feedback over agent behaviors. We show that dynamics-aware reward functions improve the sample efficiency of PbRL by an order of magnitude. In our experiments we iterate between: (1) learning a dynamics-aware state-action representation (z^{sa}) via a self-supervised temporal consistency task, and (2) bootstrapping the preference-based reward function from (z^{sa}), which results in faster policy learning and better final policy performance. For example, on quadruped-walk, walker-walk, and cheetah-run, with 50 preference labels we achieve the same performance as existing approaches with 500 preference labels, and we recover 83\% and 66\% of ground truth reward policy performance versus only 38\% and 21\%. The performance gains demonstrate the benefits of explicitly learning a dynamics-aware reward model. Repo: https://github.com/apple/ml-reed.

In the same way that the computer vision (CV) and natural language processing (NLP) communities have developed self-supervised methods, reinforcement learning (RL) can be cast as a self-supervised problem: learning to reach any goal, without requiring human-specified rewards or labels. However, actually building a self-supervised foundation for RL faces some important challenges. Building on prior contrastive approaches to this RL problem, we conduct careful ablation experiments and discover that a shallow and wide architecture, combined with careful weight initialization and data augmentation, can significantly boost the performance of these contrastive RL approaches on challenging simulated benchmarks. Additionally, we demonstrate that, with these design decisions, contrastive approaches can solve real-world robotic manipulation tasks, with tasks being specified by a single goal image provided after training.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently demonstrated remarkable potential in enhancing the reasoning capability of Large Reasoning Models (LRMs). However, RLVR often leads to entropy collapse, resulting in premature policy convergence and performance saturation. While manipulating token-level entropy has proven effective for promoting policy exploration, we argue that the latent dynamics underlying token generation encode a far richer computational structure for steering policy optimization toward a more effective exploration-exploitation tradeoff. To enable tractable analysis and intervention of the latent dynamics of LRMs, we leverage Koopman operator theory to obtain a linearized representation of their hidden-state dynamics. This enables us to introduce Dynamic Spectral Dispersion (DSD), a new metric to quantify the heterogeneity of the model's latent dynamics, serving as a direct indicator of policy exploration. Building upon these foundations, we propose Reasoning with Latent eXploration (ReLaX), a paradigm that explicitly incorporates latent dynamics to regulate exploration and exploitation during policy optimization. Comprehensive experiments across a wide range of multimodal and text-only reasoning benchmarks show that ReLaX significantly mitigates premature convergence and consistently achieves state-of-the-art performance.

Behavior constrained policy optimization has been demonstrated to be a successful paradigm for tackling Offline Reinforcement Learning. By exploiting historical transitions, a policy is trained to maximize a learned value function while constrained by the behavior policy to avoid a significant distributional shift. In this paper, we propose our closed-form policy improvement operators. We make a novel observation that the behavior constraint naturally motivates the use of first-order Taylor approximation, leading to a linear approximation of the policy objective. Additionally, as practical datasets are usually collected by heterogeneous policies, we model the behavior policies as a Gaussian Mixture and overcome the induced optimization difficulties by leveraging the LogSumExp's lower bound and Jensen's Inequality, giving rise to a closed-form policy improvement operator. We instantiate offline RL algorithms with our novel policy improvement operators and empirically demonstrate their effectiveness over state-of-the-art algorithms on the standard D4RL benchmark. Our code is available at https://cfpi-icml23.github.io/.

In large language model (LLM)-based recommendation systems, direct preference optimization (DPO) effectively aligns recommendations with user preferences, requiring multi-negative objective functions to leverage abundant implicit-feedback negatives and sharpen preference boundaries. However, our empirical analyses reveal a counterintuitive phenomenon, preference optimization collapse, where increasing the number of negative samples can lead to performance degradation despite a continuously decreasing training loss. We further theoretically demonstrate that this collapse arises from gradient suppression, caused by the dominance of easily discriminable negatives over boundary-critical negatives that truly define user preference boundaries. As a result, boundary-relevant signals are under-optimized, weakening the model's decision boundary. Motivated by these observations, we propose DynamicPO (Dynamic Preference Optimization), a lightweight and plug-and-play framework comprising two adaptive mechanisms: Dynamic Boundary Negative Selection, which identifies and prioritizes informative negatives near the model's decision boundary, and Dual-Margin Dynamic beta Adjustment, which calibrates optimization strength per sample according to boundary ambiguity. Extensive experiments on three public datasets show that DynamicPO effectively prevents optimization collapse and improves recommendation accuracy on multi-negative preference optimization methods, with negligible computational overhead. Our code and datasets are available at https://github.com/xingyuHuxingyu/DynamicPO.

As Reinforcement Learning (RL) agents are increasingly employed in diverse decision-making problems using reward preferences, it becomes important to ensure that policies learned by these frameworks in mapping observations to a probability distribution of the possible actions are explainable. However, there is little to no work in the systematic understanding of these complex policies in a contrastive manner, i.e., what minimal changes to the policy would improve/worsen its performance to a desired level. In this work, we present COUNTERPOL, the first framework to analyze RL policies using counterfactual explanations in the form of minimal changes to the policy that lead to the desired outcome. We do so by incorporating counterfactuals in supervised learning in RL with the target outcome regulated using desired return. We establish a theoretical connection between Counterpol and widely used trust region-based policy optimization methods in RL. Extensive empirical analysis shows the efficacy of COUNTERPOL in generating explanations for (un)learning skills while keeping close to the original policy. Our results on five different RL environments with diverse state and action spaces demonstrate the utility of counterfactual explanations, paving the way for new frontiers in designing and developing counterfactual policies.

The growing safety concerns surrounding large language models raise an urgent need to align them with diverse human preferences to simultaneously enhance their helpfulness and safety. A promising approach is to enforce safety constraints through Reinforcement Learning from Human Feedback (RLHF). For such constrained RLHF, typical Lagrangian-based primal-dual policy optimization methods are computationally expensive and often unstable. This paper presents a perspective of dualization that reduces constrained alignment to an equivalent unconstrained alignment problem. We do so by pre-optimizing a smooth and convex dual function that has a closed form. This shortcut eliminates the need for cumbersome primal-dual policy iterations, greatly reducing the computational burden and improving training stability. Our strategy leads to two practical algorithms in model-based and preference-based settings (MoCAN and PeCAN, respectively). A broad range of experiments demonstrate the effectiveness and merits of our algorithms.

Policy gradient methods hold great potential for solving complex continuous control tasks. Still, their training efficiency can be improved by exploiting structure within the optimization problem. Recent work indicates that supervised learning can be accelerated by leveraging the fact that gradients lie in a low-dimensional and slowly-changing subspace. In this paper, we conduct a thorough evaluation of this phenomenon for two popular deep policy gradient methods on various simulated benchmark tasks. Our results demonstrate the existence of such gradient subspaces despite the continuously changing data distribution inherent to reinforcement learning. These findings reveal promising directions for future work on more efficient reinforcement learning, e.g., through improving parameter-space exploration or enabling second-order optimization.

In multi-agent tasks, the central challenge lies in the dynamic adaptation of strategies. However, directly conditioning on opponents' strategies is intractable in the prevalent deep reinforcement learning paradigm due to a fundamental ``representational bottleneck'': neural policies are opaque, high-dimensional parameter vectors that are incomprehensible to other agents. In this work, we propose a paradigm shift that bridges this gap by representing policies as human-interpretable source code and utilizing Large Language Models (LLMs) as approximate interpreters. This programmatic representation allows us to operationalize the game-theoretic concept of Program Equilibrium. We reformulate the learning problem by utilizing LLMs to perform optimization directly in the space of programmatic policies. The LLM functions as a point-wise best-response operator that iteratively synthesizes and refines the ego agent's policy code to respond to the opponent's strategy. We formalize this process as Programmatic Iterated Best Response (PIBR), an algorithm where the policy code is optimized by textual gradients, using structured feedback derived from game utility and runtime unit tests. We demonstrate that this approach effectively solves several standard coordination matrix games and a cooperative Level-Based Foraging environment.

In recent years, various powerful policy gradient algorithms have been proposed in deep reinforcement learning. While all these algorithms build on the Policy Gradient Theorem, the specific design choices differ significantly across algorithms. We provide a holistic overview of on-policy policy gradient algorithms to facilitate the understanding of both their theoretical foundations and their practical implementations. In this overview, we include a detailed proof of the continuous version of the Policy Gradient Theorem, convergence results and a comprehensive discussion of practical algorithms. We compare the most prominent algorithms on continuous control environments and provide insights on the benefits of regularization. All code is available at https://github.com/Matt00n/PolicyGradientsJax.

As LLMs advance, post-training reinforcement learning (RL) increasingly relies on multi-dimensional rewards to cultivate comprehensive capabilities. This shift demands new algorithms capable of optimizing diverse and potentially competing objectives simultaneously. To address this, existing methods such as Group reward-Decoupled Policy Optimization (GDPO) decompose the overall score into independent reward groups, then compute the RL loss separately within each group. However, this strategy still encounters multi-reward conflicts: a single rollout can yield positive advantages on certain reward dimensions but negative ones on others, causing opposing signals to cancel each other out during aggregation, further hindering RL training efficiency. Inspired by Dynamic sAmpling Policy Optimization (DAPO), which improves RL training efficiency by filtering out ineffective rollouts with near-zero advantages, we propose Group-Dynamic reward-Decoupled Policy Optimization (GD^2PO). Specifically, GD^2PO employs a conflict-aware filtering mechanism to mask out rollouts suffering from severe reward-wise disagreement. By preventing conflicting signals from canceling each other out, this masking strategy preserves and enhances the magnitude of effective RL advantages, thereby significantly accelerating learning efficiency. Furthermore, we introduce query-level reweighting to dynamically adjust the update intensity of each query based on its overall reward consensus. Experiments on various multi-reward scenarios, including tool calling and human preference alignment, demonstrate that GD^2PO consistently and significantly outperforms existing baselines. The code is available at https://github.com/Qwen-Applications/GD2PO.

Reinforcement learning with verifiable rewards has become a central tool for improving the reasoning ability of large language models, but current methods face a trade-off between simplicity and credit assignment. Group-relative methods such as GRPO avoid training a critic, but typically assign a trajectory-level advantage to every token. Actor-critic methods provide denser learning signals, but require a learned value function with its own training instability. We introduce VIMPO, a critic-free policy optimization method that derives a policy-implied value function from the optimality conditions of KL-regularized reinforcement learning. For autoregressive generation, the resulting value recurrence can be written in terms of policy-reference log-ratios and anchored by the terminal condition that no future reward remains at the end of a trajectory. This gives a simple value loss that incorporates outcome-level verifiable rewards without training a critic. The same derivation also yields a critic-free actor advantage, allowing VIMPO to separate reward incorporation through the value loss from policy improvement through a PPO-style actor update. On mathematical RLVR benchmarks, VIMPO improves over GRPO across MATH-500, AIME 2024, AIME 2025, and OlympiadBench, with especially larger gains on competition-style evaluations. Under noisy rewards, VIMPO retains a consistent advantage over GRPO, suggesting that policy-implied value optimization can provide finer credit assignment while preserving the practical simplicity of critic-free training.

Recent advances in large vision-language models (LVLMs) have shown promise for embodied task planning, yet they struggle with fundamental challenges like dependency constraints and efficiency. Existing approaches either solely optimize action selection or leverage world models during inference, overlooking the benefits of learning to model the world as a way to enhance planning capabilities. We propose Dual Preference Optimization (D^2PO), a new learning framework that jointly optimizes state prediction and action selection through preference learning, enabling LVLMs to understand environment dynamics for better planning. To automatically collect trajectories and stepwise preference data without human annotation, we introduce a tree search mechanism for extensive exploration via trial-and-error. Extensive experiments on VoTa-Bench demonstrate that our D^2PO-based method significantly outperforms existing methods and GPT-4o when applied to Qwen2-VL (7B), LLaVA-1.6 (7B), and LLaMA-3.2 (11B), achieving superior task success rates with more efficient execution paths.

Model-based reinforcement learning (RL) can be effectively supported at scale through the use of world models. However, in practice, scaling such approaches remains fundamentally limited. A commonly recognized challenge is model bias and error compounding, which degrade long-horizon predictions. Beyond these issues, we identify a more critical yet underexplored bottleneck: a structural misalignment between search and value learning in existing world model approaches. In particular, policy improvement often relies on value functions induced by a separate, non-search policy, resulting in training inconsistency and ultimately suboptimal learning. To address this limitation, we propose Model-Based Diffusion Policy Optimization (MBDPO) in world models, a framework that unifies search and policy optimization through diffusion policy representations, thereby unlocking the potential of world models for scalable policy learning. Instead of constructing an explicit planner over a learned world model, we reformulate policy optimization as a diffusion process over searched trajectories in latent world models. In this view, we extract an implicit energy function from the collected dataset that anchors the policy, enabling MBDPO to refine the score field for policy optimization while mitigating misalignment. We evaluate MBDPO across a wide range of settings, including multi-task offline pretraining, online learning, and offline-to-online fine-tuning. In the offline regime, we further investigate its scaling behavior by pretraining on large-scale datasets, observing consistent and monotonic performance gains with increasing model capacity.

We introduce CPPO, a Contrastive Perception Policy Optimization method for finetuning vision-language models (VLMs). While reinforcement learning (RL) has advanced reasoning in language models, extending it to multimodal reasoning requires improving both the perception and reasoning aspects. Prior works tackle this challenge mainly with explicit perception rewards, but disentangling perception tokens from reasoning tokens is difficult, requiring extra LLMs, ground-truth data, forced separation of perception from reasoning by policy model, or applying rewards indiscriminately to all output tokens. CPPO addresses this problem by detecting perception tokens via entropy shifts in the model outputs under perturbed input images. CPPO then extends the RL objective function with a Contrastive Perception Loss (CPL) that enforces consistency under information-preserving perturbations and sensitivity under information-removing ones. Experiments show that CPPO surpasses previous perception-rewarding methods, while avoiding extra models, making training more efficient and scalable.

While originally developed for continuous control problems, Proximal Policy Optimization (PPO) has emerged as the work-horse of a variety of reinforcement learning (RL) applications including the fine-tuning of generative models. Unfortunately, PPO requires multiple heuristics to enable stable convergence (e.g. value networks, clipping) and is notorious for its sensitivity to the precise implementation of these components. In response, we take a step back and ask what a minimalist RL algorithm for the era of generative models would look like. We propose REBEL, an algorithm that cleanly reduces the problem of policy optimization to regressing the relative rewards via a direct policy parameterization between two completions to a prompt, enabling strikingly lightweight implementation. In theory, we prove that fundamental RL algorithms like Natural Policy Gradient can be seen as variants of REBEL, which allows us to match the strongest known theoretical guarantees in terms of convergence and sample complexity in the RL literature. REBEL can also cleanly incorporate offline data and handle the intransitive preferences we frequently see in practice. Empirically, we find that REBEL provides a unified approach to language modeling and image generation with stronger or similar performance as PPO and DPO, all while being simpler to implement and more computationally tractable than PPO.

We argue that inventory management presents unique opportunities for the reliable application of deep reinforcement learning (DRL). To enable this, we emphasize and test two complementary techniques. The first is Hindsight Differentiable Policy Optimization (HDPO), which uses pathwise gradients from offline counterfactual simulations to directly and efficiently optimize policy performance. Unlike standard policy gradient methods that rely on high-variance score-function estimators, HDPO computes gradients by differentiating through the known system dynamics. Via extensive benchmarking, we show that HDPO recovers near-optimal policies in settings with known or bounded optima, is more robust than variants of the REINFORCE algorithm, and significantly outperforms generalized newsvendor heuristics on problems using real time series data. Our second technique aligns neural policy architectures with the topology of the inventory network. We exploit Graph Neural Networks (GNNs) as a natural inductive bias for encoding supply chain structure, demonstrate that they can represent optimal and near-optimal policies in two theoretical settings, and empirically show that they reduce data requirements across six diverse inventory problems. A key obstacle to progress in this area is the lack of standardized benchmark problems. To address this gap, we open-source a suite of benchmark environments, along with our full codebase, to promote transparency and reproducibility. All resources are available at github.com/MatiasAlvo/Neural_inventory_control.

Reinforcement learning (RL) has emerged as a powerful tool for fine-tuning large language models (LLMs) to improve complex reasoning abilities. However, state-of-the-art policy optimization methods often suffer from high computational overhead and memory consumption, primarily due to the need for multiple generations per prompt and the reliance on critic networks or advantage estimates of the current policy. In this paper, we propose A*-PO, a novel two-stage policy optimization framework that directly approximates the optimal advantage function and enables efficient training of LLMs for reasoning tasks. In the first stage, we leverage offline sampling from a reference policy to estimate the optimal value function V*, eliminating the need for costly online value estimation. In the second stage, we perform on-policy updates using a simple least-squares regression loss with only a single generation per prompt. Theoretically, we establish performance guarantees and prove that the KL-regularized RL objective can be optimized without requiring complex exploration strategies. Empirically, A*-PO achieves competitive performance across a wide range of mathematical reasoning benchmarks, while reducing training time by up to 2times and peak memory usage by over 30% compared to PPO, GRPO, and REBEL. Implementation of A*-PO can be found at https://github.com/ZhaolinGao/A-PO.

Learning domain adaptive policies that can generalize to unseen transition dynamics, remains a fundamental challenge in learning-based control. Substantial progress has been made through domain representation learning to capture domain-specific information, thus enabling domain-aware decision making. We analyze the process of learning domain representations through dynamical prediction and find that selecting contexts adjacent to the current step causes the learned representations to entangle static domain information with varying dynamical properties. Such mixture can confuse the conditioned policy, thereby constraining zero-shot adaptation. To tackle the challenge, we propose DADP (Domain Adaptive Diffusion Policy), which achieves robust adaptation through unsupervised disentanglement and domain-aware diffusion injection. First, we introduce Lagged Context Dynamical Prediction, a strategy that conditions future state estimation on a historical offset context; by increasing this temporal gap, we unsupervisedly disentangle static domain representations by filtering out transient properties. Second, we integrate the learned domain representations directly into the generative process by biasing the prior distribution and reformulating the diffusion target. Extensive experiments on challenging benchmarks across locomotion and manipulation demonstrate the superior performance, and the generalizability of DADP over prior methods. More visualization results are available on the https://outsider86.github.io/DomainAdaptiveDiffusionPolicy/.

We propose Dynamic Rank Reinforcement Learning (DR-RL), a novel framework that adaptively optimizes the low-rank factorization of Multi-Head Self-Attention (MHSA) in Large Language Models (LLMs) through the integration of reinforcement learning and online matrix perturbation theory. While traditional low-rank approximations often rely on static rank assumptions--limiting their flexibility across diverse input contexts--our method dynamically selects ranks based on real-time sequence dynamics, layer-specific sensitivities, and hardware constraints. The core innovation lies in an RL agent that formulates rank selection as a sequential policy optimization problem, where the reward function strictly balances attention fidelity against computational latency. Crucially, we employ online matrix perturbation bounds to enable incremental rank updates, thereby avoiding the prohibitive cost of full decomposition during inference. Furthermore, the integration of a lightweight Transformer-based policy network and batched Singular Value Decomposition (SVD) operations ensures scalable deployment on modern GPU architectures. Experiments demonstrate that DR-RL maintains downstream accuracy statistically equivalent to full-rank attention while significantly reducing Floating Point Operations (FLOPs), particularly in long-sequence regimes (L > 4096). This work bridges the gap between adaptive efficiency and theoretical rigor in MHSA, offering a principled, mathematically grounded alternative to heuristic rank reduction techniques in resource-constrained deep learning. Source code and experiment logs are available at: https://github.com/canererden/DR_RL_Project

We propose Q-learning with Adjoint Matching (QAM), a novel TD-based reinforcement learning (RL) algorithm that tackles a long-standing challenge in continuous-action RL: efficient optimization of an expressive diffusion or flow-matching policy with respect to a parameterized Q-function. Effective optimization requires exploiting the first-order information of the critic, but it is challenging to do so for flow or diffusion policies because direct gradient-based optimization via backpropagation through their multi-step denoising process is numerically unstable. Existing methods work around this either by only using the value and discarding the gradient information, or by relying on approximations that sacrifice policy expressivity or bias the learned policy. QAM sidesteps both of these challenges by leveraging adjoint matching, a recently proposed technique in generative modeling, which transforms the critic's action gradient to form a step-wise objective function that is free from unstable backpropagation, while providing an unbiased, expressive policy at the optimum. Combined with temporal-difference backup for critic learning, QAM consistently outperforms prior approaches on hard, sparse reward tasks in both offline and offline-to-online RL.

The shift toward interacting with frozen, "black-box" Large Language Models (LLMs) has transformed prompt engineering from a heuristic exercise into a critical optimization challenge. We propose a Reinforcement Learning (RL) framework for training learned prompting policies via iterative distillation of experience. In this architecture, a lightweight prompter model is optimized to maximize task-specific rewards for a larger, frozen worker LLM. By utilizing a contrastive experience buffer that couples scalar rewards with dense textual critiques, our approach effectively amortizes iterative prompt refinement into single-shot policy weights. Our experimental analysis focuses on the Big Bench Extra Hard (BBEH) and Tau-bench suites, covering a diverse range of multi-step reasoning and tool-use tasks. We demonstrate significant gains, improving performance from 55% to 90% in logic-intensive reasoning and 74% to 91% in tool-use tasks. Furthermore, we analyze the structural evolution of prompts, demonstrating how the policy discovers specialized algorithmic heuristics. We provide comprehensive comparisons against state-of-the-art evolutionary baselines like GEPA, showing that iterative distillation achieves superior performance with higher sample efficiency.

Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks, and (2) the design of good heuristics or approximation algorithms often requires significant manual trial-and-error. In this work, we argue that data-driven strategies can automate this process and learn efficient algorithms without compromising optimality. To do so, we present network control problems through the lens of reinforcement learning and propose a graph network-based framework to handle a broad class of problems. Instead of naively computing actions over high-dimensional graph elements, e.g., edges, we propose a bi-level formulation where we (1) specify a desired next state via RL, and (2) solve a convex program to best achieve it, leading to drastically improved scalability and performance. We further highlight a collection of desirable features to system designers, investigate design decisions, and present experiments on real-world control problems showing the utility, scalability, and flexibility of our framework.

Reinforcement learning from human feedback (RLHF) is the canonical framework for large language model alignment. However, rising popularity in offline alignment algorithms challenge the need for on-policy sampling in RLHF. Within the context of reward over-optimization, we start with an opening set of experiments that demonstrate the clear advantage of online methods over offline methods. This prompts us to investigate the causes to the performance discrepancy through a series of carefully designed experimental ablations. We show empirically that hypotheses such as offline data coverage and data quality by itself cannot convincingly explain the performance difference. We also find that while offline algorithms train policy to become good at pairwise classification, it is worse at generations; in the meantime the policies trained by online algorithms are good at generations while worse at pairwise classification. This hints at a unique interplay between discriminative and generative capabilities, which is greatly impacted by the sampling process. Lastly, we observe that the performance discrepancy persists for both contrastive and non-contrastive loss functions, and appears not to be addressed by simply scaling up policy networks. Taken together, our study sheds light on the pivotal role of on-policy sampling in AI alignment, and hints at certain fundamental challenges of offline alignment algorithms.

Reinforcement learning from human feedback (RLHF) methods are emerging as a way to fine-tune diffusion models (DMs) for visual generation. However, commonly used on-policy strategies are limited by the generalization capability of the reward model, while off-policy approaches require large amounts of difficult-to-obtain paired human-annotated data, particularly in visual generation tasks. To address the limitations of both on- and off-policy RLHF, we propose a preference optimization method that aligns DMs with preferences without relying on reward models or paired human-annotated data. Specifically, we introduce a Semi-Policy Preference Optimization (SePPO) method. SePPO leverages previous checkpoints as reference models while using them to generate on-policy reference samples, which replace "losing images" in preference pairs. This approach allows us to optimize using only off-policy "winning images." Furthermore, we design a strategy for reference model selection that expands the exploration in the policy space. Notably, we do not simply treat reference samples as negative examples for learning. Instead, we design an anchor-based criterion to assess whether the reference samples are likely to be winning or losing images, allowing the model to selectively learn from the generated reference samples. This approach mitigates performance degradation caused by the uncertainty in reference sample quality. We validate SePPO across both text-to-image and text-to-video benchmarks. SePPO surpasses all previous approaches on the text-to-image benchmarks and also demonstrates outstanding performance on the text-to-video benchmarks. Code will be released in https://github.com/DwanZhang-AI/SePPO.

The alignment of language models with human preferences is vital for their application in real-world tasks. The problem is formulated as optimizing the model's policy to maximize the expected reward that reflects human preferences with minimal deviation from the initial policy. While considered as a straightforward solution, reinforcement learning (RL) suffers from high variance in policy updates, which impedes efficient policy improvement. Recently, direct preference optimization (DPO) was proposed to directly optimize the policy from preference data. Though simple to implement, DPO is derived based on the optimal policy that is not assured to be achieved in practice, which undermines its convergence to the intended solution. In this paper, we propose efficient exact optimization (EXO) of the alignment objective. We prove that EXO is guaranteed to optimize in the same direction as the RL algorithms asymptotically for arbitary parametrization of the policy, while enables efficient optimization by circumventing the complexities associated with RL algorithms. We compare our method to DPO with both theoretical and empirical analyses, and further demonstrate the advantages of our method over existing approaches on realistic human preference data.

With the rapid advancement of large language models (LLMs), aligning policy models with human preferences has become increasingly critical. Direct Preference Optimization (DPO) has emerged as a promising approach for alignment, acting as an RL-free alternative to Reinforcement Learning from Human Feedback (RLHF). Despite DPO's various advancements and inherent limitations, an in-depth review of these aspects is currently lacking in the literature. In this work, we present a comprehensive review of the challenges and opportunities in DPO, covering theoretical analyses, variants, relevant preference datasets, and applications. Specifically, we categorize recent studies on DPO based on key research questions to provide a thorough understanding of DPO's current landscape. Additionally, we propose several future research directions to offer insights on model alignment for the research community.

This paper provides a self-contained, from-scratch, exposition of key algorithms for instruction tuning of models: SFT, Rejection Sampling, REINFORCE, Trust Region Policy Optimization (TRPO), Proximal Policy Optimization (PPO), Group Relative Policy Optimization (GRPO), and Direct Preference Optimization (DPO). Explanations of these algorithms often assume prior knowledge, lack critical details, and/or are overly generalized and complex. Here, each method is discussed and developed step by step using simplified and explicit notation focused on LLMs, aiming to eliminate ambiguity and provide a clear and intuitive understanding of the concepts. By minimizing detours into the broader RL literature and connecting concepts to LLMs, we eliminate superfluous abstractions and reduce cognitive overhead. Following this exposition, we provide a literature review of new techniques and approaches beyond those detailed. Finally, new ideas for research and exploration in the form of GRAPE (Generalized Relative Advantage Policy Evolution) are presented.

Large Language Models (LLMs) exhibit robust problem-solving capabilities for diverse tasks. However, most LLM-based agents are designed as specific task solvers with sophisticated prompt engineering, rather than agents capable of learning and evolving through interactions. These task solvers necessitate manually crafted prompts to inform task rules and regulate LLM behaviors, inherently incapacitating to address complex dynamic scenarios e.g., large interactive games. In light of this, we propose Agent-Pro: an LLM-based Agent with Policy-level Reflection and Optimization that can learn a wealth of expertise from interactive experiences and progressively elevate its behavioral policy. Specifically, it involves a dynamic belief generation and reflection process for policy evolution. Rather than action-level reflection, Agent-Pro iteratively reflects on past trajectories and beliefs, fine-tuning its irrational beliefs for a better policy. Moreover, a depth-first search is employed for policy optimization, ensuring continual enhancement in policy payoffs. Agent-Pro is evaluated across two games: Blackjack and Texas Hold'em, outperforming vanilla LLM and specialized models. Our results show Agent-Pro can learn and evolve in complex and dynamic scenes, which also benefits numerous LLM-based applications.

We investigate whether self-supervised learning (SSL) can improve online reinforcement learning (RL) from pixels. We extend the contrastive reinforcement learning framework (e.g., CURL) that jointly optimizes SSL and RL losses and conduct an extensive amount of experiments with various self-supervised losses. Our observations suggest that the existing SSL framework for RL fails to bring meaningful improvement over the baselines only taking advantage of image augmentation when the same amount of data and augmentation is used. We further perform evolutionary searches to find the optimal combination of multiple self-supervised losses for RL, but find that even such a loss combination fails to meaningfully outperform the methods that only utilize carefully designed image augmentations. After evaluating these approaches together in multiple different environments including a real-world robot environment, we confirm that no single self-supervised loss or image augmentation method can dominate all environments and that the current framework for joint optimization of SSL and RL is limited. Finally, we conduct the ablation study on multiple factors and demonstrate the properties of representations learned with different approaches.

We describe an iterative procedure for optimizing policies, with guaranteed monotonic improvement. By making several approximations to the theoretically-justified procedure, we develop a practical algorithm, called Trust Region Policy Optimization (TRPO). This algorithm is similar to natural policy gradient methods and is effective for optimizing large nonlinear policies such as neural networks. Our experiments demonstrate its robust performance on a wide variety of tasks: learning simulated robotic swimming, hopping, and walking gaits; and playing Atari games using images of the screen as input. Despite its approximations that deviate from the theory, TRPO tends to give monotonic improvement, with little tuning of hyperparameters.

Multi-preference optimization enriches language-model alignment beyond pairwise preferences by contrasting entire sets of helpful and undesired responses, thereby enabling richer training signals for large language models. During self-play alignment, these models often produce numerous candidate answers per query, rendering it computationally infeasible to include all responses in the training objective. In this work, we propose Active Multi-Preference Optimization (AMPO), a novel approach that combines on-policy generation, a multi-preference group-contrastive loss, and active subset selection. Specifically, we score and embed large candidate pools of responses and then select a small, yet informative, subset that covers reward extremes and distinct semantic clusters for preference optimization. Our contrastive training scheme is capable of identifying not only the best and worst answers but also subtle, underexplored modes that are crucial for robust alignment. Theoretically, we provide guarantees for expected reward maximization using our active selection method, and empirically, AMPO achieves state-of-the-art results on AlpacaEval using Llama 8B.

Discovering achievements with a hierarchical structure in procedurally generated environments presents a significant challenge. This requires an agent to possess a broad range of abilities, including generalization and long-term reasoning. Many prior methods have been built upon model-based or hierarchical approaches, with the belief that an explicit module for long-term planning would be advantageous for learning hierarchical dependencies. However, these methods demand an excessive number of environment interactions or large model sizes, limiting their practicality. In this work, we demonstrate that proximal policy optimization (PPO), a simple yet versatile model-free algorithm, outperforms previous methods when optimized with recent implementation practices. Moreover, we find that the PPO agent can predict the next achievement to be unlocked to some extent, albeit with limited confidence. Based on this observation, we introduce a novel contrastive learning method, called achievement distillation, which strengthens the agent's ability to predict the next achievement. Our method exhibits a strong capacity for discovering hierarchical achievements and shows state-of-the-art performance on the challenging Crafter environment in a sample-efficient manner while utilizing fewer model parameters.

Designing control policies whose performance level is guaranteed to remain above a given threshold in a span of environments is a critical feature for the adoption of reinforcement learning (RL) in real-world applications. The search for such robust policies is a notoriously difficult problem, related to the so-called dynamic model of transition function uncertainty, where the environment dynamics are allowed to change at each time step. But in practical cases, one is rather interested in robustness to a span of static transition models throughout interaction episodes. The static model is known to be harder to solve than the dynamic one, and seminal algorithms, such as robust value iteration, as well as most recent works on deep robust RL, build upon the dynamic model. In this work, we propose to revisit the static model. We suggest an analysis of why solving the static model under some mild hypotheses is a reasonable endeavor, based on an equivalence with the dynamic model, and formalize the general intuition that robust MDPs can be solved by tackling a series of static problems. We introduce a generic meta-algorithm called IWOCS, which incrementally identifies worst-case transition models so as to guide the search for a robust policy. Discussion on IWOCS sheds light on new ways to decouple policy optimization and adversarial transition functions and opens new perspectives for analysis. We derive a deep RL version of IWOCS and demonstrate it is competitive with state-of-the-art algorithms on classical benchmarks.

Reinforcement Learning, particularly through policy gradient methods, has played a central role in enabling reasoning capabilities of Large Language Models. However, the optimization stability of policy gradients in this setting remains understudied. As a result, existing implementations often resort to conservative hyperparameter choices to ensure stability, which requires more training samples and increases computational costs. Hence, developing models for reliably tracking the underlying optimization dynamics and leveraging them into training enables more sample-efficient regimes and further unleashes scalable post-training. We address this gap by formalizing the stochastic optimization problem of policy gradients with explicit consideration of second-order geometry. We propose a tractable computational framework that tracks and leverages curvature information during policy updates. We further employ this framework to design interventions in the optimization process through data selection. The resultant algorithm, Curvature-Aware Policy Optimization (CAPO), identifies samples that contribute to unstable updates and masks them out. Theoretically, we establish monotonic improvement guarantees under realistic assumptions. On standard math reasoning benchmarks, we empirically show that CAPO ensures stable updates under aggressive learning regimes where baselines catastrophically fail. With minimal intervention (rejecting fewer than 8% of tokens), CAPO achieves up to 30x improvement in sample efficiency over standard GRPO for LLM reasoning.

We present Premier-TACO, a multitask feature representation learning approach designed to improve few-shot policy learning efficiency in sequential decision-making tasks. Premier-TACO leverages a subset of multitask offline datasets for pretraining a general feature representation, which captures critical environmental dynamics and is fine-tuned using minimal expert demonstrations. It advances the temporal action contrastive learning (TACO) objective, known for state-of-the-art results in visual control tasks, by incorporating a novel negative example sampling strategy. This strategy is crucial in significantly boosting TACO's computational efficiency, making large-scale multitask offline pretraining feasible. Our extensive empirical evaluation in a diverse set of continuous control benchmarks including Deepmind Control Suite, MetaWorld, and LIBERO demonstrate Premier-TACO's effectiveness in pretraining visual representations, significantly enhancing few-shot imitation learning of novel tasks. Our code, pretraining data, as well as pretrained model checkpoints will be released at https://github.com/PremierTACO/premier-taco.

Communication is a powerful tool for coordination in multi-agent RL. But inducing an effective, common language is a difficult challenge, particularly in the decentralized setting. In this work, we introduce an alternative perspective where communicative messages sent between agents are considered as different incomplete views of the environment state. By examining the relationship between messages sent and received, we propose to learn to communicate using contrastive learning to maximize the mutual information between messages of a given trajectory. In communication-essential environments, our method outperforms previous work in both performance and learning speed. Using qualitative metrics and representation probing, we show that our method induces more symmetric communication and captures global state information from the environment. Overall, we show the power of contrastive learning and the importance of leveraging messages as encodings for effective communication.

Natural language is often the easiest and most convenient modality for humans to specify tasks for robots. However, learning to ground language to behavior typically requires impractical amounts of diverse, language-annotated demonstrations collected on each target robot. In this work, we aim to separate the problem of what to accomplish from how to accomplish it, as the former can benefit from substantial amounts of external observation-only data, and only the latter depends on a specific robot embodiment. To this end, we propose Video-Language Critic, a reward model that can be trained on readily available cross-embodiment data using contrastive learning and a temporal ranking objective, and use it to score behavior traces from a separate actor. When trained on Open X-Embodiment data, our reward model enables 2x more sample-efficient policy training on Meta-World tasks than a sparse reward only, despite a significant domain gap. Using in-domain data but in a challenging task generalization setting on Meta-World, we further demonstrate more sample-efficient training than is possible with prior language-conditioned reward models that are either trained with binary classification, use static images, or do not leverage the temporal information present in video data.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a popular paradigm for aligning models with human intent. Typically RLHF algorithms operate in two phases: first, use human preferences to learn a reward function and second, align the model by optimizing the learned reward via reinforcement learning (RL). This paradigm assumes that human preferences are distributed according to reward, but recent work suggests that they instead follow the regret under the user's optimal policy. Thus, learning a reward function from feedback is not only based on a flawed assumption of human preference, but also leads to unwieldy optimization challenges that stem from policy gradients or bootstrapping in the RL phase. Because of these optimization challenges, contemporary RLHF methods restrict themselves to contextual bandit settings (e.g., as in large language models) or limit observation dimensionality (e.g., state-based robotics). We overcome these limitations by introducing a new family of algorithms for optimizing behavior from human feedback using the regret-based model of human preferences. Using the principle of maximum entropy, we derive Contrastive Preference Learning (CPL), an algorithm for learning optimal policies from preferences without learning reward functions, circumventing the need for RL. CPL is fully off-policy, uses only a simple contrastive objective, and can be applied to arbitrary MDPs. This enables CPL to elegantly scale to high-dimensional and sequential RLHF problems while being simpler than prior methods.

Policy Optimization (PO) is one of the most popular methods in Reinforcement Learning (RL). Thus, theoretical guarantees for PO algorithms have become especially important to the RL community. In this paper, we study PO in adversarial MDPs with a challenge that arises in almost every real-world application -- delayed bandit feedback. We give the first near-optimal regret bounds for PO in tabular MDPs, and may even surpass state-of-the-art (which uses less efficient methods). Our novel Delay-Adapted PO (DAPO) is easy to implement and to generalize, allowing us to extend our algorithm to: (i) infinite state space under the assumption of linear Q-function, proving the first regret bounds for delayed feedback with function approximation. (ii) deep RL, demonstrating its effectiveness in experiments on MuJoCo domains.

Reinforcement Learning has emerged as a post-training approach to elicit agentic RAG behaviors such as search and planning from language models. However, compact language models (e.g., 0.5B parameters) struggle due to poor reasoning ability, resulting in sparse rewards and unstable training. To overcome these difficulties, we propose Distillation-Guided Policy Optimization (DGPO), which addresses the challenges through cold-start initialization from teacher demonstrations and continuous teacher guidance during policy optimization. To systematically evaluate our approach, we introduce Agentic RAG Capabilities (ARC), a fine-grained metric analyzing reasoning, search coordination, and response synthesis. Comprehensive experiments demonstrate that DGPO enables compact models to achieve sophisticated agentic search behaviors, even outperforming the larger teacher model in some cases. DGPO makes agentic RAG feasible in computing resource-constrained environments.

The current dominant paradigm in sensorimotor control, whether imitation or reinforcement learning, is to train policies directly in raw action spaces such as torque, joint angle, or end-effector position. This forces the agent to make decisions individually at each timestep in training, and hence, limits the scalability to continuous, high-dimensional, and long-horizon tasks. In contrast, research in classical robotics has, for a long time, exploited dynamical systems as a policy representation to learn robot behaviors via demonstrations. These techniques, however, lack the flexibility and generalizability provided by deep learning or reinforcement learning and have remained under-explored in such settings. In this work, we begin to close this gap and embed the structure of a dynamical system into deep neural network-based policies by reparameterizing action spaces via second-order differential equations. We propose Neural Dynamic Policies (NDPs) that make predictions in trajectory distribution space as opposed to prior policy learning methods where actions represent the raw control space. The embedded structure allows end-to-end policy learning for both reinforcement and imitation learning setups. We show that NDPs outperform the prior state-of-the-art in terms of either efficiency or performance across several robotic control tasks for both imitation and reinforcement learning setups. Project video and code are available at https://shikharbahl.github.io/neural-dynamic-policies/

Temporal-difference (TD) methods learn state and action values efficiently by bootstrapping from their own future value predictions, but such a self-bootstrapping mechanism is prone to bootstrapping bias, where the errors in the value targets accumulate across steps and result in biased value estimates. Recent work has proposed to use chunked critics, which estimate the value of short action sequences ("chunks") rather than individual actions, speeding up value backup. However, extracting policies from chunked critics is challenging: policies must output the entire action chunk open-loop, which can be sub-optimal for environments that require policy reactivity and also challenging to model especially when the chunk length grows. Our key insight is to decouple the chunk length of the critic from that of the policy, allowing the policy to operate over shorter action chunks. We propose a novel algorithm that achieves this by optimizing the policy against a distilled critic for partial action chunks, constructed by optimistically backing up from the original chunked critic to approximate the maximum value achievable when a partial action chunk is extended to a complete one. This design retains the benefits of multi-step value propagation while sidestepping both the open-loop sub-optimality and the difficulty of learning action chunking policies for long action chunks. We evaluate our method on challenging, long-horizon offline goal-conditioned tasks and show that it reliably outperforms prior methods. Code: github.com/ColinQiyangLi/dqc.

While scaling individual Large Language Models (LLMs) has delivered remarkable progress, the next frontier lies in scaling collaboration through multi-agent systems (MAS). However, purely autonomous MAS remain ''closed-world'' systems, constrained by the static knowledge horizon of pre-trained models. This limitation makes them brittle on tasks requiring knowledge beyond training data, often leading to collective failure under novel challenges. To address this, we propose the Human-In-the-Loop Multi-Agent Collaboration (HILA) framework, a principled paradigm for human--agent collaboration. HILA trains agents to learn a metacognitive policy that governs when to solve problems autonomously and when to defer to a human expert. To operationalize this policy, we introduce Dual-Loop Policy Optimization, which disentangles immediate decision-making from long-term capability growth. The inner loop applies Group Relative Policy Optimization (GRPO) with a cost-aware reward to optimize deferral decisions, while the outer loop implements continual learning, transforming expert feedback into high-quality supervised signals that strengthen the agent's reasoning ability. Experiments on challenging mathematical and problem-solving benchmarks show that HILA, equipped with Dual-Loop Policy Optimization, consistently outperforms advanced MAS, establishing a principled foundation for collaborative and continually improving agentic systems.

We investigate the temporal concatenation of sub-policies in Markov Decision Processes (MDP) with time-varying reward functions. We introduce General Dijkstra Search (GDS), and prove that globally optimal goal-reaching policies can be recovered through temporal composition of intermediate optimal sub-policies. Motivated by the "search, select, update" principle underlying GDS, we propose Dynamic Latent Routing (DLR), a language-model post-training method that jointly learns discrete latent codes, routing policies, and model parameters through dynamic search in a single training stage. In low-data fine-tuning settings, DLR matches or outperforms supervised fine-tuning across four datasets and six models, achieving a mean gain of +6.6 percentage points, while prior discrete-latent baselines consistently underperform SFT. Mechanistic analyses and targeted code ablations show that DLR learns structured routing behaviors with distinct causal roles.

Predicting and reasoning about the future lie at the heart of many time-series questions. For example, goal-conditioned reinforcement learning can be viewed as learning representations to predict which states are likely to be visited in the future. While prior methods have used contrastive predictive coding to model time series data, learning representations that encode long-term dependencies usually requires large amounts of data. In this paper, we introduce a temporal difference version of contrastive predictive coding that stitches together pieces of different time series data to decrease the amount of data required to learn predictions of future events. We apply this representation learning method to derive an off-policy algorithm for goal-conditioned RL. Experiments demonstrate that, compared with prior RL methods, ours achieves 2 times median improvement in success rates and can better cope with stochastic environments. In tabular settings, we show that our method is about 20 times more sample efficient than the successor representation and 1500 times more sample efficient than the standard (Monte Carlo) version of contrastive predictive coding.

We consider the problem of multi-objective alignment of foundation models with human preferences, which is a critical step towards helpful and harmless AI systems. However, it is generally costly and unstable to fine-tune large foundation models using reinforcement learning (RL), and the multi-dimensionality, heterogeneity, and conflicting nature of human preferences further complicate the alignment process. In this paper, we introduce Rewards-in-Context (RiC), which conditions the response of a foundation model on multiple rewards in its prompt context and applies supervised fine-tuning for alignment. The salient features of RiC are simplicity and adaptivity, as it only requires supervised fine-tuning of a single foundation model and supports dynamic adjustment for user preferences during inference time. Inspired by the analytical solution of an abstracted convex optimization problem, our dynamic inference-time adjustment method approaches the Pareto-optimal solution for multiple objectives. Empirical evidence demonstrates the efficacy of our method in aligning both Large Language Models (LLMs) and diffusion models to accommodate diverse rewards with only around 10% GPU hours compared with multi-objective RL baseline.

We introduce distributional dynamic programming (DP) methods for optimizing statistical functionals of the return distribution, with standard reinforcement learning as a special case. Previous distributional DP methods could optimize the same class of expected utilities as classic DP. To go beyond expected utilities, we combine distributional DP with stock augmentation, a technique previously introduced for classic DP in the context of risk-sensitive RL, where the MDP state is augmented with a statistic of the rewards obtained so far (since the first time step). We find that a number of recently studied problems can be formulated as stock-augmented return distribution optimization, and we show that we can use distributional DP to solve them. We analyze distributional value and policy iteration, with bounds and a study of what objectives these distributional DP methods can or cannot optimize. We describe a number of applications outlining how to use distributional DP to solve different stock-augmented return distribution optimization problems, for example maximizing conditional value-at-risk, and homeostatic regulation. To highlight the practical potential of stock-augmented return distribution optimization and distributional DP, we combine the core ideas of distributional value iteration with the deep RL agent DQN, and empirically evaluate it for solving instances of the applications discussed.

Reinforcement Learning has become a standard paradigm for aligning Large Language Models with human intent and task requirements. While Group Relative Policy Optimization offers an efficient, value-model-free alternative to Proximal Policy Optimization, adapting it to real-world multi-reward settings remains challenging. Standard scalarization practices, such as Reward Combination and Advantage Combination, suffer from significant drawbacks: Reward Combination frequently generates advantages with excessively large squared magnitudes that lead to training instability, while Advantage Combination relies on static hyperparameters and ignores cross-objective correlations. To address these limitations, we propose Dynamic Variance-adaptive Advantage Optimization (DVAO), which dynamically adjusts combination weights based on the empirical reward variance of each objective within a rollout group, effectively up-weighting objectives with a stronger learning signal while suppressing noisy ones. We mathematically prove that DVAO maintains bounded advantage magnitudes for stable training and introduces a self-adaptive cross-objective regularization mechanism. Extensive experiments on mathematical reasoning and tool-use benchmarks using Qwen3 and Qwen2.5 models demonstrate that DVAO significantly outperforms baseline methods, achieving a superior multi-objective Pareto frontier and robust training stability.

Reinforcement learning (RL) has become a cornerstone for fine-tuning Large Language Models (LLMs), with Proximal Policy Optimization (PPO) serving as the de facto standard algorithm. Despite its ubiquity, we argue that the core ratio clipping mechanism in PPO is structurally ill-suited for the large vocabularies inherent to LLMs. PPO constrains policy updates based on the probability ratio of sampled tokens, which serves as a noisy single-sample Monte Carlo estimate of the true policy divergence. This creates a sub-optimal learning dynamic: updates to low-probability tokens are aggressively over-penalized, while potentially catastrophic shifts in high-probability tokens are under-constrained, leading to training inefficiency and instability. To address this, we propose Divergence Proximal Policy Optimization (DPPO), which substitutes heuristic clipping with a more principled constraint based on a direct estimate of policy divergence (e.g., Total Variation or KL). To avoid huge memory footprint, we introduce the efficient Binary and Top-K approximations to capture the essential divergence with negligible overhead. Extensive empirical evaluations demonstrate that DPPO achieves superior training stability and efficiency compared to existing methods, offering a more robust foundation for RL-based LLM fine-tuning.

Ensuring that large language models (LLMs) are both helpful and harmless is a critical challenge, as overly strict constraints can lead to excessive refusals, while permissive models risk generating harmful content. Existing approaches, such as reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO), attempt to balance these trade-offs but suffer from performance conflicts, limited controllability, and poor extendability. To address these issues, we propose Preference Vector, a novel framework inspired by task arithmetic. Instead of optimizing multiple preferences within a single objective, we train separate models on individual preferences, extract behavior shifts as preference vectors, and dynamically merge them at test time. This modular approach enables fine-grained, user-controllable preference adjustments and facilitates seamless integration of new preferences without retraining. Experiments show that our proposed Preference Vector framework improves helpfulness without excessive conservatism, allows smooth control over preference trade-offs, and supports scalable multi-preference alignment.

Reinforcement learning (RL) is vital for optimizing large language models (LLMs). Recent Group Relative Policy Optimization (GRPO) estimates advantages using multiple on-policy outputs per prompt, leading to high computational costs and low data efficiency. To address this, we introduce Replay-Enhanced Policy Optimization (RePO), which leverages diverse replay strategies to retrieve off-policy samples from a replay buffer, allowing policy optimization based on a broader and more diverse set of samples for each prompt. Experiments on five LLMs across seven mathematical reasoning benchmarks demonstrate that RePO achieves absolute average performance gains of 18.4 and 4.1 points for Qwen2.5-Math-1.5B and Qwen3-1.7B, respectively, compared to GRPO. Further analysis indicates that RePO increases computational cost by 15% while raising the number of effective optimization steps by 48% for Qwen3-1.7B, with both on-policy and off-policy sample numbers set to 8. The repository can be accessed at https://github.com/SihengLi99/RePO.

Reinforcement learning is a framework for learning to act sequentially in an unknown environment. We propose a natural approach for modeling policy structure in policy gradients. The key idea is to optimize for a subset of future rewards: smaller subsets represent simpler policies, which can be learned more reliably because their empirical gradient estimates are more accurate. Our approach allows for modeling and comparison of different policy classes, including full planning, greedy, K-step lookahead, and segment policies. We evaluate the policies empirically on multiple persona-alignment conversational problems. Different policies excel in different problems, reflecting their different characteristics and highlighting the importance of our studied policy class.

Contrastive Learning has recently received interest due to its success in self-supervised representation learning in the computer vision domain. However, the origins of Contrastive Learning date as far back as the 1990s and its development has spanned across many fields and domains including Metric Learning and natural language processing. In this paper we provide a comprehensive literature review and we propose a general Contrastive Representation Learning framework that simplifies and unifies many different contrastive learning methods. We also provide a taxonomy for each of the components of contrastive learning in order to summarise it and distinguish it from other forms of machine learning. We then discuss the inductive biases which are present in any contrastive learning system and we analyse our framework under different views from various sub-fields of Machine Learning. Examples of how contrastive learning has been applied in computer vision, natural language processing, audio processing, and others, as well as in Reinforcement Learning are also presented. Finally, we discuss the challenges and some of the most promising future research directions ahead.

Prior works in multi-objective reinforcement learning typically use linear reward scalarization with fixed weights, which provably fail to capture non-convex Pareto fronts and thus yield suboptimal results. This limitation becomes especially critical in online preference alignment for large language models. Here, stochastic trajectories generated by parameterized policies create highly non-linear and non-convex mappings from parameters to objectives that no single static weighting scheme can find optimal trade-offs. We address this limitation by introducing dynamic reward weighting, which adaptively adjusts reward weights during the online reinforcement learning process. Unlike existing approaches that rely on fixed-weight interpolation, our dynamic weighting continuously balances and prioritizes objectives in training, facilitating effective exploration of Pareto fronts in objective space. We introduce two approaches of increasing sophistication and generalizability: (1) hypervolume-guided weight adaptation and (2) gradient-based weight optimization, offering a versatile toolkit for online multi-objective alignment. Our extensive experiments demonstrate their compatibility with commonly used online reinforcement learning algorithms (including GRPO, REINFORCE, and RLOO), effectiveness across multiple mathematical reasoning datasets, and applicability to different model families, consistently achieving Pareto dominant solutions with fewer training steps than fixed-weight linear scalarization baselines.

On-policy reinforcement learning (RL), particularly Proximal Policy Optimization (PPO) and Group Relative Policy Optimization (GRPO), has become the dominant paradigm for fine-tuning large language models (LLMs). While policy ratio clipping stabilizes training, this heuristic hard constraint incurs a fundamental cost: it indiscriminately truncates gradients from high-return yet high-divergence actions, suppressing rare but highly informative "eureka moments" in complex reasoning. Moreover, once data becomes slightly stale, hard clipping renders it unusable, leading to severe sample inefficiency. In this work, we revisit the trust-region objective in policy optimization and show that explicitly constraining the variance (second central moment) of the policy ratio provides a principled and smooth relaxation of hard clipping. This distributional constraint stabilizes policy updates while preserving gradient signals from valuable trajectories. Building on this insight, we propose R^2VPO (Ratio-Variance Regularized Policy Optimization), a novel primal-dual framework that supports stable on-policy learning and enables principled off-policy data reuse by dynamically reweighting stale samples rather than discarding them. We extensively evaluate R^2VPO on fine-tuning state-of-the-art LLMs, including DeepSeek-Distill-Qwen-1.5B and the openPangu-Embedded series (1B and 7B), across challenging mathematical reasoning benchmarks. Experimental results show that R^2VPO consistently achieves superior asymptotic performance, with average relative gains of up to 17% over strong clipping-based baselines, while requiring approximately 50% fewer rollouts to reach convergence. These findings establish ratio-variance control as a promising direction for improving both stability and data efficiency in RL-based LLM alignment.

Critique-guided reinforcement learning (RL) has emerged as a powerful paradigm for training LLM agents by augmenting sparse outcome rewards with natural-language feedback. However, current methods often rely on static or offline critic models, which fail to adapt as the policy evolves. In on-policy RL, the agent's error patterns shift over time, causing stationary critics to become stale and providing feedback of diminishing utility. To address this, we introduce ECHO (Evolving Critic for Hindsight-Guided Optimization)}, a framework that jointly optimizes the policy and critic through a synchronized co-evolutionary loop. ECHO utilizes a cascaded rollout mechanism where the critic generates multiple diagnoses for an initial trajectory, followed by policy refinement to enable group-structured advantage estimation. We address the challenge of learning plateaus via a saturation-aware gain shaping objective, which rewards the critic for inducing incremental improvements in high-performing trajectories. By employing dual-track GRPO updates, ECHO ensures the critic's feedback stays synchronized with the evolving policy. Experimental results show that ECHO yields more stable training and higher long-horizon task success across open-world environments.

Large Language Models (LLMs) can acquire extensive world knowledge through pre-training on large corpora. However, due to exposure to low-quality data, LLMs may exhibit harmful behavior without aligning with human values. The dominant approach for steering LLMs towards beneficial behavior involves Reinforcement Learning with Human Feedback (RLHF), with Proximal Policy Optimization (PPO) serving as the default RL optimizer. Despite its effectiveness, PPO has limitations when optimizing rewards trained from comparison-based loss. Primarily, PPO is not invariant to equivalent reward functions containing identical preference information due to the need to calibrate the reward scale. Additionally, PPO's necessity for token-wise updates introduces complexity in both function approximation and algorithm design compared to trajectory-wise optimization. This paper proposes a new framework, reinforcement learning with relative feedback, and a novel trajectory-wise policy gradient algorithm, Pairwise Proximal Policy Optimization (P3O) that operates directly on comparative rewards. We show theoretically that P3O is invariant to equivalent rewards and avoids the complexity of PPO. Empirical evaluations demonstrate that P3O outperforms PPO in the KL-Reward trade-off and can align with human preferences as well as or better than prior methods. In summary, this work introduces a simpler yet effective approach for aligning LLMs to human preferences through relative feedback.

Recent advances at the intersection of reinforcement learning (RL) and visual intelligence have enabled agents that not only perceive complex visual scenes but also reason, generate, and act within them. This survey offers a critical and up-to-date synthesis of the field. We first formalize visual RL problems and trace the evolution of policy-optimization strategies from RLHF to verifiable reward paradigms, and from Proximal Policy Optimization to Group Relative Policy Optimization. We then organize more than 200 representative works into four thematic pillars: multi-modal large language models, visual generation, unified model frameworks, and vision-language-action models. For each pillar we examine algorithmic design, reward engineering, benchmark progress, and we distill trends such as curriculum-driven training, preference-aligned diffusion, and unified reward modeling. Finally, we review evaluation protocols spanning set-level fidelity, sample-level preference, and state-level stability, and we identify open challenges that include sample efficiency, generalization, and safe deployment. Our goal is to provide researchers and practitioners with a coherent map of the rapidly expanding landscape of visual RL and to highlight promising directions for future inquiry. Resources are available at: https://github.com/weijiawu/Awesome-Visual-Reinforcement-Learning.

Direct Preference Optimization (DPO) and its variants have become standard for aligning Large Language Models due to their simplicity and offline stability. However, we identify two fundamental limitations. First, the optimal policy depends on arbitrary modeling choices (scalarization function, reference policy), yielding behavior reflecting parameterization artifacts rather than true preferences. Second, treating response generation in isolation fails to leverage comparative information in pairwise data, leaving the model's capacity for intrinsic self-reflection untapped. To address it, we propose Intrinsic Self-reflective Preference Optimization (InSPO), deriving a globally optimal policy conditioning on both context and alternative responses. We prove this formulation superior to DPO/RLHF while guaranteeing invariance to scalarization and reference choices. InSPO serves as a plug-and-play enhancement without architectural changes or inference overhead. Experiments demonstrate consistent improvements in win rates and length-controlled metrics, validating that unlocking self-reflection yields more robust, human-aligned LLMs. Our Code is available at https://github.com/Skylanding/InSPO.

Model-free reinforcement learning algorithms have seen remarkable progress, but key challenges remain. Trust Region Policy Optimization (TRPO) is known for ensuring monotonic policy improvement through conservative updates within a trust region, backed by strong theoretical guarantees. However, its reliance on complex second-order optimization limits its practical efficiency. Proximal Policy Optimization (PPO) addresses this by simplifying TRPO's approach using ratio clipping, improving efficiency but sacrificing some theoretical robustness. This raises a natural question: Can we combine the strengths of both methods? In this paper, we introduce Simple Policy Optimization (SPO), a novel unconstrained first-order algorithm. By slightly modifying the policy loss used in PPO, SPO can achieve the best of both worlds. Our new objective improves upon ratio clipping, offering stronger theoretical properties and better constraining the probability ratio within the trust region. Empirical results demonstrate that SPO outperforms PPO with a simple implementation, particularly for training large, complex network architectures end-to-end.

Large language model (LLM)-based agents have recently shown impressive progress in a variety of domains, including open-ended conversation and multi-step decision-making. However, applying these agents to social deduction games such as Werewolf, which requires both strategic decision-making and free-form language interaction, remains non-trivial. Traditional methods based on Counterfactual Regret Minimization (CFR) or reinforcement learning (RL) typically depend on a predefined action space, making them unsuitable for language games with unconstrained text action space. Meanwhile, pure LLM-based agents often suffer from intrinsic biases and require prohibitively large datasets for fine-tuning. We propose Latent Space Policy Optimization (LSPO), an iterative framework that addresses these challenges by first mapping free-form text to a discrete latent space, where methods like CFR and RL can learn strategic policy more effectively. We then translate the learned policy back into natural language dialogues, which are used to fine-tune an LLM via Direct Preference Optimization (DPO). By iteratively alternating between these stages, our LSPO agent progressively enhances both strategic reasoning and language communication. Experiment results on the Werewolf game show that our method improves the agent's performance in each iteration and outperforms existing Werewolf agents, underscoring its promise for free-form language decision-making.

Language models must now generalize out of the box to novel environments and work inside inference-scaling search procedures, such as AlphaEvolve, that select rollouts with a variety of task-specific reward functions. Unfortunately, the standard paradigm of LLM post-training optimizes a pre-specified scalar reward, often leading current LLMs to produce low-entropy response distributions and thus to struggle at displaying the diversity that inference-time search will require. We propose Vector Policy Optimization (VPO), an RL algorithm that explicitly trains policies to anticipate diverse downstream reward functions and to produce diverse solutions. VPO exploits that rewards are often vector-valued in practice, like per-test-case correctness in code generation or, say, multiple different user personas or reward models. VPO is essentially a drop-in replacement for the GRPO advantage estimator, but it trains the LLM to output a set of solutions where individual solutions specialize to different trade-offs in the vector reward space. Across four tasks, VPO matches or beats the strongest scalar RL baselines on test-time search (e.g. pass@k and best@k), with the gap widening as the search budget grows. For evolutionary search, VPO models unlock problems that GRPO models cannot solve at all. As test-time search becomes more standardized, optimizing for diversity may need to become the default post-training objective.

Direct Preference Optimization (DPO) has emerged as a lightweight and effective alternative to Reinforcement Learning from Human Feedback (RLHF) and Reinforcement Learning with AI Feedback (RLAIF) for aligning large language and vision-language models. However, the standard DPO formulation, in which both the chosen and rejected responses are generated by the same policy, suffers from a weak learning signal because the two responses often share similar errors and exhibit small Kullback-Leibler (KL) divergence. This leads to slow and unstable convergence. To address this limitation, we introduce Reflective Preference Optimization (RPO), a new framework that incorporates hint-guided reflection into the DPO paradigm. RPO uses external models to identify hallucination sources and generate concise reflective hints, enabling the construction of on-policy preference pairs with stronger contrastiveness and clearer preference signals. We theoretically show that conditioning on hints increases the expected preference margin through mutual information and improves sample efficiency while remaining within the policy distribution family. Empirically, RPO achieves superior alignment with fewer training samples and iterations, substantially reducing hallucination rates and delivering state-of-the-art performance across multimodal benchmarks.

Augmenting large language models (LLMs) with external tools is a promising approach to enhance their capabilities. Effectively leveraging this potential for complex tasks hinges crucially on improving their ability to use tools. Synthesizing tool use data by simulating the real world is an effective approach. Nevertheless, our investigation reveals that training gains significantly decay as the scale of these data increases. The primary factor is the model's poor performance (a.k.a deficiency) in complex scenarios, which hinders learning from data using SFT. Driven by this objective, we propose an iterative reinforced fine-tuning strategy to continually guide the model to alleviate it. Specifically, we first identify deficiency-related data based on feedback from the policy model, then perform a Monte Carlo Tree Search to collect fine-grained preference pairs to pinpoint deficiencies. Subsequently, we update the policy model using preference optimization to align with ground truth and misalign with deficiencies. This process can be iterated. Moreover, before the iteration, we propose an easy-to-hard warm-up SFT strategy to facilitate learning from challenging data. The experiments demonstrate our models go beyond the same parametric models, outperforming many larger open-source and closed-source models. Additionally, it has achieved notable training gains in complex tool use scenarios.

Tremendous progress has been made in reinforcement learning (RL) over the past decade. Most of these advancements came through the continual development of new algorithms, which were designed using a combination of mathematical derivations, intuitions, and experimentation. Such an approach of creating algorithms manually is limited by human understanding and ingenuity. In contrast, meta-learning provides a toolkit for automatic machine learning method optimisation, potentially addressing this flaw. However, black-box approaches which attempt to discover RL algorithms with minimal prior structure have thus far not outperformed existing hand-crafted algorithms. Mirror Learning, which includes RL algorithms, such as PPO, offers a potential middle-ground starting point: while every method in this framework comes with theoretical guarantees, components that differentiate them are subject to design. In this paper we explore the Mirror Learning space by meta-learning a "drift" function. We refer to the immediate result as Learnt Policy Optimisation (LPO). By analysing LPO we gain original insights into policy optimisation which we use to formulate a novel, closed-form RL algorithm, Discovered Policy Optimisation (DPO). Our experiments in Brax environments confirm state-of-the-art performance of LPO and DPO, as well as their transfer to unseen settings.

Two major sources of training data exist for post-training modern language models: online (model-generated rollouts) data, and offline (human or other-model demonstrations) data. These two types of data are typically used by approaches like Reinforcement Learning (RL) and Supervised Fine-Tuning (SFT), respectively. In this paper, we show that these approaches are not in contradiction, but are instances of a single optimization process. We derive a Unified Policy Gradient Estimator, and present the calculations of a wide spectrum of post-training approaches as the gradient of a common objective under different data distribution assumptions and various bias-variance tradeoffs. The gradient estimator is constructed with four interchangeable parts: stabilization mask, reference policy denominator, advantage estimate, and likelihood gradient. Motivated by our theoretical findings, we propose Hybrid Post-Training (HPT), an algorithm that dynamically selects different training signals. HPT is designed to yield both effective exploitation of demonstration and stable exploration without sacrificing learned reasoning patterns. We provide extensive experiments and ablation studies to verify the effectiveness of our unified theoretical framework and HPT. Across six mathematical reasoning benchmarks and two out-of-distribution suites, HPT consistently surpasses strong baselines across models of varying scales and families.

The Base-New Trade-off (BNT) problem universally exists during the optimization of CLIP-based prompt tuning, where continuous fine-tuning on base (target) classes leads to a simultaneous decrease of generalization ability on new (unseen) classes. Existing approaches attempt to regulate the prompt tuning process to balance BNT by appending constraints. However, imposed on the same target prompt, these constraints fail to fully avert the mutual exclusivity between the optimization directions for base and new. As a novel solution to this challenge, we propose the plug-and-play Dual-Prompt Collaboration (DPC) framework, the first that decoupling the optimization processes of base and new tasks at the prompt level. Specifically, we clone a learnable parallel prompt based on the backbone prompt, and introduce a variable Weighting-Decoupling framework to independently control the optimization directions of dual prompts specific to base or new tasks, thus avoiding the conflict in generalization. Meanwhile, we propose a Dynamic Hard Negative Optimizer, utilizing dual prompts to construct a more challenging optimization task on base classes for enhancement. For interpretability, we prove the feature channel invariance of the prompt vector during the optimization process, providing theoretical support for the Weighting-Decoupling of DPC. Extensive experiments on multiple backbones demonstrate that DPC can significantly improve base performance without introducing any external knowledge beyond the base classes, while maintaining generalization to new classes. Code is available at: https://github.com/JREion/DPC.

Large language models are typically post-trained using supervised fine-tuning (SFT) and reinforcement learning (RL), yet effectively unifying efficient knowledge injection with robust generalization remains challenging. In this work, we provide a training-dynamics analysis showing that SFT can be interpreted as a special case of policy gradient optimization with an extremely sparse implicit reward and unstable inverse-probability weighting, which together lead to single-path dependency, entropy collapse, and gradient explosion. Motivated by this diagnosis, we propose Group Fine-Tuning (GFT), a unified post-training framework that addresses these intrinsic limitations through two mechanisms: Group Advantage Learning, which constructs diverse response groups and derives normalized contrastive supervision to alleviate reward sparsity, and Dynamic Coefficient Rectification, which adaptively bounds inverse-probability weights to stabilize optimization while preserving efficient knowledge injection. Experiments demonstrate that GFT consistently surpasses SFT-based methods and yields policies that integrate more smoothly with subsequent RL training.

Streaming autoregressive (AR) video generators combined with few-step distillation achieve low-latency, high-quality synthesis, yet remain difficult to align via reinforcement learning from human feedback (RLHF). Existing SDE-based GRPO methods face challenges in this setting: few-step ODEs and consistency model samplers deviate from standard flow-matching ODEs, and their short, low-stochasticity trajectories are highly sensitive to initialization noise, rendering intermediate SDE exploration ineffective. We propose AR-CoPO (AutoRegressive Contrastive Policy Optimization), a framework that adapts the Neighbor GRPO contrastive perspective to streaming AR generation. AR-CoPO introduces chunk-level alignment via a forking mechanism that constructs neighborhood candidates at a randomly selected chunk, assigns sequence-level rewards, and performs localized GRPO updates. We further propose a semi-on-policy training strategy that complements on-policy exploration with exploitation over a replay buffer of reference rollouts, improving generation quality across domains. Experiments on Self-Forcing demonstrate that AR-CoPO improves both out-of-domain generalization and in-domain human preference alignment over the baseline, providing evidence of genuine alignment rather than reward hacking.

Large Language Models (LLMs) employ multi-turn interaction as a fundamental paradigm for completing complex tasks. However, their performance often degrades in extended interactions, as they are typically trained on static, single-turn data, which hinders their ability to adapt to real-time user feedback. To address this limitation, we first propose a new paradigm: Test-Time Policy Adaptation for Multi-Turn Interactions (T2PAM), which utilizes user feedback from the ongoing interaction as a reward signal to estimate a latent optimal policy aligned with user preferences, then updates a small subset of parameters to steer the model toward this policy, ultimately enabling efficient in-conversation self-correction. We then introduce Optimum-Referenced One-Step Adaptation (ROSA), a lightweight algorithm that operationalizes T2PAM. ROSA guides the model parameters toward a theoretical optimal policy in a single, efficient update step, avoiding costly iterative gradient-based optimization and minimizing computational overhead. We provide a rigorous theoretical analysis guaranteeing that the policy of ROSA converges to the preference of user as the number of interactions increases. Extensive experiments on challenging benchmark demonstrate that ROSA achieves significant improvements in both task effectiveness and efficiency.

While Large Language Model (LLM) agents excel at general tasks, they inherently struggle with continual adaptation due to the frozen weights after deployment. Conventional reinforcement learning (RL) offers a solution but incurs prohibitive computational costs and the risk of catastrophic forgetting. We introduce Just-In-Time Reinforcement Learning (JitRL), a training-free framework that enables test-time policy optimization without any gradient updates. JitRL maintains a dynamic, non-parametric memory of experiences and retrieves relevant trajectories to estimate action advantages on-the-fly. These estimates are then used to directly modulate the LLM's output logits. We theoretically prove that this additive update rule is the exact closed-form solution to the KL-constrained policy optimization objective. Extensive experiments on WebArena and Jericho demonstrate that JitRL establishes a new state-of-the-art among training-free methods. Crucially, JitRL outperforms the performance of computationally expensive fine-tuning methods (e.g., WebRL) while reducing monetary costs by over 30 times, offering a scalable path for continual learning agents. The code is available at https://github.com/liushiliushi/JitRL.

Drawing upon recent advances in language model alignment, we formulate offline Reinforcement Learning as a two-stage optimization problem: First pretraining expressive generative policies on reward-free behavior datasets, then fine-tuning these policies to align with task-specific annotations like Q-values. This strategy allows us to leverage abundant and diverse behavior data to enhance generalization and enable rapid adaptation to downstream tasks using minimal annotations. In particular, we introduce Efficient Diffusion Alignment (EDA) for solving continuous control problems. EDA utilizes diffusion models for behavior modeling. However, unlike previous approaches, we represent diffusion policies as the derivative of a scalar neural network with respect to action inputs. This representation is critical because it enables direct density calculation for diffusion models, making them compatible with existing LLM alignment theories. During policy fine-tuning, we extend preference-based alignment methods like Direct Preference Optimization (DPO) to align diffusion behaviors with continuous Q-functions. Our evaluation on the D4RL benchmark shows that EDA exceeds all baseline methods in overall performance. Notably, EDA maintains about 95\% of performance and still outperforms several baselines given only 1\% of Q-labelled data during fine-tuning.

Reinforcement learning with verifiable rewards (RLVR) has become a standard approach for large language models (LLMs) post-training to incentivize reasoning capacity. Among existing recipes, group-based policy gradient is prevalent, which samples a group of responses per prompt and updates the policy via group-relative advantage signals. This work reveals that these optimization strategies share a common geometric structure: each implicitly defines a target distribution on the response simplex and projects toward it via first-order approximation. Building on this insight, we propose Listwise Policy Optimization (LPO) to explicitly conduct the target-projection, which demystifies the implicit target by restricting the proximal RL objective to the response simplex, and then projects the policy via exact divergence minimization. This framework provides (i) monotonic improvement on the listwise objective with bounded, zero-sum, and self-correcting projection gradients, and (ii) flexibility in divergence selection with distinct structural properties through the decoupled projection step. On diverse reasoning tasks and LLM backbones, LPO consistently improves training performance over typical policy gradient baselines under matched targets, while intrinsically preserving optimization stability and response diversity.

Reward-based alignment methods for large language models (LLMs) face two key limitations: vulnerability to reward hacking, where models exploit flaws in the reward signal; and reliance on brittle, labor-intensive prompt engineering when LLMs are used as reward models. We introduce Meta Policy Optimization (MPO), a framework that addresses these challenges by integrating a meta-reward model that dynamically refines the reward model's prompt throughout training. In MPO, the meta-reward model monitors the evolving training context and continuously adjusts the reward model's prompt to maintain high alignment, providing an adaptive reward signal that resists exploitation by the policy. This meta-learning approach promotes a more stable policy optimization, and greatly reduces the need for manual reward prompt design. It yields performance on par with or better than models guided by extensively hand-crafted reward prompts. Furthermore, we show that MPO maintains its effectiveness across diverse tasks, such as question answering and mathematical reasoning, without requiring specialized reward designs. Beyond standard RLAIF, MPO's meta-learning formulation is readily extensible to higher-level alignment frameworks. Overall, this method addresses theoretical and practical challenges in reward-based RL alignment for LLMs, paving the way for more robust and adaptable alignment strategies. The code and models will be publicly shared.

This work presents In-Context Policy Iteration, an algorithm for performing Reinforcement Learning (RL), in-context, using foundation models. While the application of foundation models to RL has received considerable attention, most approaches rely on either (1) the curation of expert demonstrations (either through manual design or task-specific pretraining) or (2) adaptation to the task of interest using gradient methods (either fine-tuning or training of adapter layers). Both of these techniques have drawbacks. Collecting demonstrations is labor-intensive, and algorithms that rely on them do not outperform the experts from which the demonstrations were derived. All gradient techniques are inherently slow, sacrificing the "few-shot" quality that made in-context learning attractive to begin with. In this work, we present an algorithm, ICPI, that learns to perform RL tasks without expert demonstrations or gradients. Instead we present a policy-iteration method in which the prompt content is the entire locus of learning. ICPI iteratively updates the contents of the prompt from which it derives its policy through trial-and-error interaction with an RL environment. In order to eliminate the role of in-weights learning (on which approaches like Decision Transformer rely heavily), we demonstrate our algorithm using Codex, a language model with no prior knowledge of the domains on which we evaluate it.

In this paper, we propose to use deep policy networks which are trained with an advantage actor-critic method for statistically optimised dialogue systems. First, we show that, on summary state and action spaces, deep Reinforcement Learning (RL) outperforms Gaussian Processes methods. Summary state and action spaces lead to good performance but require pre-engineering effort, RL knowledge, and domain expertise. In order to remove the need to define such summary spaces, we show that deep RL can also be trained efficiently on the original state and action spaces. Dialogue systems based on partially observable Markov decision processes are known to require many dialogues to train, which makes them unappealing for practical deployment. We show that a deep RL method based on an actor-critic architecture can exploit a small amount of data very efficiently. Indeed, with only a few hundred dialogues collected with a handcrafted policy, the actor-critic deep learner is considerably bootstrapped from a combination of supervised and batch RL. In addition, convergence to an optimal policy is significantly sped up compared to other deep RL methods initialized on the data with batch RL. All experiments are performed on a restaurant domain derived from the Dialogue State Tracking Challenge 2 (DSTC2) dataset.

Reinforcement learning from human feedback (RLHF) has emerged as the main paradigm for aligning large language models (LLMs) with human preferences. Typically, RLHF involves the initial step of learning a reward model from human feedback, often expressed as preferences between pairs of text generations produced by a pre-trained LLM. Subsequently, the LLM's policy is fine-tuned by optimizing it to maximize the reward model through a reinforcement learning algorithm. However, an inherent limitation of current reward models is their inability to fully represent the richness of human preferences and their dependency on the sampling distribution. In this study, we introduce an alternative pipeline for the fine-tuning of LLMs using pairwise human feedback. Our approach entails the initial learning of a preference model, which is conditioned on two inputs given a prompt, followed by the pursuit of a policy that consistently generates responses preferred over those generated by any competing policy, thus defining the Nash equilibrium of this preference model. We term this approach Nash learning from human feedback (NLHF). In the context of a tabular policy representation, we present a novel algorithmic solution, Nash-MD, founded on the principles of mirror descent. This algorithm produces a sequence of policies, with the last iteration converging to the regularized Nash equilibrium. Additionally, we explore parametric representations of policies and introduce gradient descent algorithms for deep-learning architectures. To demonstrate the effectiveness of our approach, we present experimental results involving the fine-tuning of a LLM for a text summarization task. We believe NLHF offers a compelling avenue for preference learning and policy optimization with the potential of advancing the field of aligning LLMs with human preferences.

In this work we explore a new approach for robots to teach themselves about the world simply by observing it. In particular we investigate the effectiveness of learning task-agnostic representations for continuous control tasks. We extend Time-Contrastive Networks (TCN) that learn from visual observations by embedding multiple frames jointly in the embedding space as opposed to a single frame. We show that by doing so, we are now able to encode both position and velocity attributes significantly more accurately. We test the usefulness of this self-supervised approach in a reinforcement learning setting. We show that the representations learned by agents observing themselves take random actions, or other agents perform tasks successfully, can enable the learning of continuous control policies using algorithms like Proximal Policy Optimization (PPO) using only the learned embeddings as input. We also demonstrate significant improvements on the real-world Pouring dataset with a relative error reduction of 39.4% for motion attributes and 11.1% for static attributes compared to the single-frame baseline. Video results are available at https://sites.google.com/view/actionablerepresentations .

We propose Drifting Field Policy (DFP), a non-ODE one-step generative policy built on the drifting model paradigm. We frame the policy update as a reverse-KL Wasserstein-2 gradient flow toward a soft target policy, so that each DFP update corresponds to a gradient step in probability space. By construction, this gradient is decomposed into an ascent toward higher action-value regions and a score matching with the anchor policy as a trust region. We further derive a simple, tractable surrogate of the otherwise intractable update loss, akin to behavior cloning on top-K critic-selected actions. We find empirically that this mechanism uniquely benefits the drifting backbone owing to its non-ODE parameterization. With one-step inference, DFP achieves state-of-the-art performance on several manipulation tasks across Robomimic and OGBench, outperforming ODE-based policies.

Aligning generative models with human preference via RLHF typically suffers from overoptimization, where an imperfectly learned reward model can misguide the generative model to output undesired responses. We investigate this problem in a principled manner by identifying the source of the misalignment as a form of distributional shift and uncertainty in learning human preferences. To mitigate overoptimization, we first propose a theoretical algorithm that chooses the best policy for an adversarially chosen reward model; one that simultaneously minimizes the maximum likelihood estimation of the loss and a reward penalty term. Here, the reward penalty term is introduced to prevent the policy from choosing actions with spurious high proxy rewards, resulting in provable sample efficiency of the algorithm under a partial coverage style condition. Moving from theory to practice, the proposed algorithm further enjoys an equivalent but surprisingly easy-to-implement reformulation. Using the equivalence between reward models and the corresponding optimal policy, the algorithm features a simple objective that combines: (i) a preference optimization loss that directly aligns the policy with human preference, and (ii) a supervised learning loss that explicitly imitates the policy with a (suitable) baseline distribution. In the context of aligning large language models (LLM), this objective fuses the direct preference optimization (DPO) loss with the supervised fune-tuning (SFT) loss to help mitigate the overoptimization towards undesired responses, for which we name the algorithm Regularized Preference Optimization (RPO). Experiments of aligning LLMs demonstrate the improved performance of RPO compared with DPO baselines. Our work sheds light on the interplay between preference optimization and SFT in tuning LLMs with both theoretical guarantees and empirical evidence.

Aligning large language models (LLMs) on domain-specific data remains a fundamental challenge. Supervised fine-tuning (SFT) offers a straightforward way to inject domain knowledge but often degrades the model's generality. In contrast, on-policy reinforcement learning (RL) preserves generality but fails to effectively assimilate hard samples that exceed the model's current reasoning level. Recent off-policy RL attempts improve hard sample utilization, yet they suffer from severe training instability due to the forced distribution shift toward off-policy knowledge. To reconcile effective off-policy knowledge absorption with the stability of on-policy RL, we propose Rephrasing Policy Optimization (RePO). In RePO, the policy model is prompted to first comprehend off-policy knowledge and then rephrase it into trajectories that conform to its own stylistic and parametric distribution. RePO dynamically replaces low-reward rollouts with these rephrased, high-quality trajectories. This strategy guides the model toward correct reasoning paths while strictly preserving on-policy training dynamics. Experiments on several benchmarks demonstrate that RePO improves hard-sample utilization and outperforms existing baselines, achieving state-of-the-art performance.

We study the problem of training and fine-tuning expressive policies with online reinforcement learning (RL) given an offline dataset. Training expressive policy classes with online RL present a unique challenge of stable value maximization. Unlike simpler Gaussian policies commonly used in online RL, expressive policies like diffusion and flow-matching policies are parameterized by a long denoising chain, which hinders stable gradient propagation from actions to policy parameters when optimizing against some value function. Our key insight is that we can address stable value maximization by avoiding direct optimization over value with the expressive policy and instead construct an on-the-fly RL policy to maximize Q-value. We propose Expressive Policy Optimization (EXPO), a sample-efficient online RL algorithm that utilizes an on-the-fly policy to maximize value with two parameterized policies -- a larger expressive base policy trained with a stable imitation learning objective and a light-weight Gaussian edit policy that edits the actions sampled from the base policy toward a higher value distribution. The on-the-fly policy optimizes the actions from the base policy with the learned edit policy and chooses the value maximizing action from the base and edited actions for both sampling and temporal-difference (TD) backup. Our approach yields up to 2-3x improvement in sample efficiency on average over prior methods both in the setting of fine-tuning a pretrained policy given offline data and in leveraging offline data to train online.

As autonomous agents become adept at understanding and interacting with graphical user interface (GUI) environments, a new era of automated task execution is emerging. Recent studies have demonstrated that Reinforcement Learning (RL) can effectively enhance agents' performance in dynamic interactive GUI environments. However, these methods face two key limitations: (1) they overlook the significant variation in difficulty across different GUI tasks by treating the entire training data as a uniform set, which hampers the agent's ability to adapt its learning process; and (2) most approaches collapse task-specific nuances into a single, coarse reward, leaving the agent with a uniform signal that yields inefficient policy updates. To address these limitations, we propose CRAFT-GUI, a curriculum learning framework based on Group Relative Policy Optimization (GRPO) that explicitly accounts for the varying difficulty across trajectories. To enable more fine-grained policy optimization, we design a reward function that combines simple rule-based signals with model-judged evaluation, providing richer and more nuanced feedback during training. Experimental results demonstrate that our method achieves significant improvements over previous state-of-the-art approaches, outperforming them by 5.6% on public benchmarks Android Control and 10.3% on our internal online benchmarks, respectively. These findings empirically validate the effectiveness of integrating reinforcement learning with curriculum learning in GUI interaction tasks.

Recent studies have demonstrated that Reinforcement Learning (RL), notably Group Relative Policy Optimization (GRPO), can intrinsically elicit and enhance the reasoning capabilities of Vision-Language Models (VLMs). However, despite the promise, the underlying mechanisms that drive the effectiveness of RL models as well as their limitations remain underexplored. In this paper, we highlight a fundamental behavioral distinction between RL and base models, where the former engages in deeper yet narrow reasoning, while base models, despite less refined along individual path, exhibit broader and more diverse thinking patterns. Through further analysis of training dynamics, we show that GRPO is prone to diversity collapse, causing models to prematurely converge to a limited subset of reasoning strategies while discarding the majority of potential alternatives, leading to local optima and poor scalability. To address this, we propose Multi-Group Policy Optimization (MUPO), a simple yet effective approach designed to incentivize divergent thinking across multiple solutions, and demonstrate its effectiveness on established benchmarks. Project page: https://xytian1008.github.io/MUPO/

Reinforcement learning from human feedback (RLHF) is a promising solution to align large language models (LLMs) more closely with human values. Off-policy preference optimization, where the preference data is obtained from other models, is widely adopted due to its cost efficiency and scalability. However, off-policy preference optimization often suffers from a distributional gap between the policy used for data collection and the target policy, leading to suboptimal optimization. In this paper, we propose a novel strategy to mitigate this problem by simulating on-policy learning with off-policy preference data. Our Weighted Preference Optimization (WPO) method adapts off-policy data to resemble on-policy data more closely by reweighting preference pairs according to their probability under the current policy. This method not only addresses the distributional gap problem but also enhances the optimization process without incurring additional costs. We validate our method on instruction following benchmarks including Alpaca Eval 2 and MT-bench. WPO not only outperforms Direct Preference Optimization (DPO) by up to 5.6% on Alpaca Eval 2 but also establishes a remarkable length-controlled winning rate against GPT-4-turbo of 48.6% based on Llama-3-8B-Instruct, making it the strongest 8B model on the leaderboard. We will release the code and models at https://github.com/wzhouad/WPO.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a powerful paradigm for facilitating the self-improvement of large language models (LLMs), particularly in the domain of complex reasoning tasks. However, prevailing on-policy RL methods often contend with significant training instability and inefficiency. This is primarily due to a capacity-difficulty mismatch, where the complexity of training data frequently outpaces the model's current capabilities, leading to critically sparse reward signals and stalled learning progress. This challenge is particularly acute for smaller, more resource-efficient LLMs. To overcome this, we introduce the Guided Hybrid Policy Optimization (GHPO), a novel difficulty-aware reinforcement learning framework. GHPO dynamically calibrates task difficulty by employing adaptive prompt refinement to provide targeted guidance. This unique approach adaptively balances direct imitation learning for problems currently beyond the model's reach with exploration-based reinforcement learning for more manageable tasks, effectively creating a smooth and optimized learning curriculum. Extensive experiments demonstrate that GHPO achieves an average performance gain of approximately 5% across six challenging mathematics benchmarks, consistently outperforming strong on-policy reinforcement learning and curriculum learning baselines. Further analysis confirms that our framework significantly enhances both training stability and final reasoning performance, thus offering a scalable and efficient solution for developing powerful and robust reasoning models.

Aligning language models (LMs) with curated human feedback is critical to control their behaviors in real-world applications. Several recent policy optimization methods, such as DPO and SLiC, serve as promising alternatives to the traditional Reinforcement Learning from Human Feedback (RLHF) approach. In practice, human feedback often comes in a format of a ranked list over multiple responses to amortize the cost of reading prompt. Multiple responses can also be ranked by reward models or AI feedback. There lacks such a study on directly fitting upon a list of responses. In this work, we formulate the LM alignment as a listwise ranking problem and describe the Listwise Preference Optimization (LiPO) framework, where the policy can potentially learn more effectively from a ranked list of plausible responses given the prompt. This view draws an explicit connection to Learning-to-Rank (LTR), where most existing preference optimization work can be mapped to existing ranking objectives, especially pairwise ones. Following this connection, we provide an examination of ranking objectives that are not well studied for LM alignment withDPO and SLiC as special cases when list size is two. In particular, we highlight a specific method, LiPO-{\lambda}, which leverages a state-of-the-art listwise ranking objective and weights each preference pair in a more advanced manner. We show that LiPO-{\lambda} can outperform DPO and SLiC by a clear margin on two preference alignment tasks.

Reinforcement Learning with Verifiable Rewards (RLVR) has become a central post-training paradigm for improving the reasoning capabilities of large language models. Yet existing methods share a common blind spot: they optimize policies based on instantaneous group-level or batch-level statistics without ever verifying whether the resulting update actually improved the model. This open-loop design -- updating in isolation at each step, guided only by within-group (batch) reward signals -- means optimization can drift or collapse with no mechanism to detect and correct these failures. We argue that the missing ingredient is policy improvement feedback: the ability to measure and optimize inter-iteration progress directly. To this end, we introduce Policy Improvement Reinforcement Learning (PIRL), a framework that replaces surrogate reward maximization with the explicit objective of maximizing cumulative policy improvement across iterations, and prove this temporal objective is perfectly aligned with maximizing final task performance. Building on PIRL, we propose Policy Improvement Policy Optimization (PIPO), which implements closed-loop optimization through retrospective verification. At each iteration, PIPO evaluates whether the previous update yielded genuine improvement against a sliding-window historical baseline, then actively reinforces beneficial updates and suppresses the harmful ones -- transforming an open-loop process into a self-correcting one. We provide theoretical analysis showing that PIPO performs ascent on the PIRL objective in expectation, and experiments on mathematical reasoning benchmarks demonstrate improved stability and performance over GRPO and its variants.

We investigate the challenge of parametrizing policies for reinforcement learning (RL) in high-dimensional continuous action spaces. Our objective is to develop a multimodal policy that overcomes limitations inherent in the commonly-used Gaussian parameterization. To achieve this, we propose a principled framework that models the continuous RL policy as a generative model of optimal trajectories. By conditioning the policy on a latent variable, we derive a novel variational bound as the optimization objective, which promotes exploration of the environment. We then present a practical model-based RL method, called Reparameterized Policy Gradient (RPG), which leverages the multimodal policy parameterization and learned world model to achieve strong exploration capabilities and high data efficiency. Empirical results demonstrate that our method can help agents evade local optima in tasks with dense rewards and solve challenging sparse-reward environments by incorporating an object-centric intrinsic reward. Our method consistently outperforms previous approaches across a range of tasks. Code and supplementary materials are available on the project page https://haosulab.github.io/RPG/

Reinforcement learning (RL) has emerged as a promising paradigm for inducing explicit reasoning behaviors in large language and vision-language models. However, reasoning-oriented RL post-training remains fundamentally challenging due to sparse trajectory-level rewards, leading to ambiguous credit assignment and severe exploration failures that can trap the policy in a ``learning cliff.'' Recent on-policy distillation methods introduce dense teacher supervision to stabilize optimization, but apply it uniformly across all generated trajectories. We argue that such uniform distillation is ill-suited for reasoning-intensive tasks, as low-quality on-policy trajectories often originate from early logical errors, and distillation under flawed contexts injects noisy and misaligned gradients. To address these challenges, we propose Knowledge-Enhanced Preference Optimization (KEPO), a unified post-training framework that integrates: (i) a quality-gated on-policy distillation objective that selectively applies dense teacher guidance only to high-quality trajectories, and (ii) a knowledge-enhanced exploration strategy that leverages hints learned from a teacher model to rejectively sample reward-positive on-policy trajectories for RL, thereby mitigating exploration collapse. Evaluated on a challenging medical visual question answering benchmark under single-source generalization, KEPO demonstrates improved training stability, more coherent reasoning behaviors, and superior out-of-distribution performance over reinforcement learning and on-policy distillation baselines.