Off-Policy RL

Off-policy, value-based reinforcement learning methods such as Q-learning are appealing because they can learn from arbitrary experience, including data collected by older policies or other agents. In practice, however, bootstrapping makes long-horizon learning brittle: estimation errors at later states propagate backward through temporal-difference (TD) updates and can compound over time. We propose long-horizon Q-learning (LQL), which introduces a principled backstop against compounding error when learning the optimal action-value function. LQL builds on a prior optimality tightening observation: any realized action sequence lower-bounds what the optimal policy can achieve in expectation, so acting optimally earlier should not be worse than following the observed actions for several steps before switching to optimal behavior. Our contribution is to turn this inequality into a practical stabilization mechanism for Q-learning by using a hinge loss to penalize violations of these bounds. Importantly, LQL computes these penalties using network outputs already produced for the TD error, requiring no auxiliary networks and no additional forward passes relative to Q-learning. When combined with multiple state-of-the-art methods on a range of online and offline-to-online benchmarks, LQL consistently outperforms both 1-step TD and n-step TD learning at similar runtime.

Generative control policies (GCPs), such as diffusion- and flow-based control policies, have emerged as effective parameterizations for robot learning. This work introduces Off-policy Generative Policy Optimization (OGPO), a sample-efficient algorithm for finetuning GCPs that maintains off-policy critic networks to maximize data reuse and propagate policy gradients through the full generative process of the policy via a modified PPO objective, using critics as the terminal reward. OGPO achieves state-of-the-art performance on manipulation tasks spanning multi-task settings, high-precision insertion, and dexterous control. To our knowledge, it is also the only method that can fine-tune poorly-initialized behavior cloning policies to near full task-success with no expert data in the online replay buffer, and does so with few task-specific hyperparameter tuning. Through extensive empirical investigations, we demonstrate that OGPO drastically outperforms methods alternatives on policy steering and learning residual corrections, and identify the key mechanisms behind its performance. We further introduce practical stabilization tricks, including success-buffer regularization, two-sided conservative advantages, and Q-variance reduction, to mitigate critic over-exploitation across state- and pixel-based settings. Beyond proposing OGPO, we conduct a systematic empirical study of GCP finetuning, identifying the stabilizing mechanisms and failure modes that govern successful off-policy full-policy improvement.

Reinforcement learning with verifiable rewards (RLVR) is a core post-training recipe for reasoning models, yet pure on-policy learning can be inefficient when useful trajectories are difficult to discover or exploration narrows. Existing self-guided approaches largely reuse capability already available to the current or earlier learner. We instead ask whether learning can also make use of capabilities that emerge later in training: can a model learn from its own future self? We introduce temporal self-distillation, in which a policy receives guidance from a stronger later checkpoint of itself. We hypothesize that the most useful temporal teacher need not be the strongest one: a teacher must provide sufficiently new capability while remaining compatible enough for that capability to be readily transferred, motivating a near-future regime. We study this principle through two complementary mechanisms. Near-Future Policy Optimization (NPO) performs off-policy behavioral transfer using verified future-self trajectories, while Near-Future Policy Distillation (NPD) performs on-policy token-level transfer on learner-generated trajectories. We further introduce AutoNPO, which adaptively determines when temporal guidance is useful and how far to roll back, turning future-self guidance into a repeated self-bootstrap process. Across eight image-text benchmarks, NPO improves GRPO from 60.25 to 62.84 and AutoNPO reaches 63.15, with consistent gains on text-only and video reasoning. Under NPD, a near-future teacher reaches 63.23 after continued RL versus 61.92 with a far-future teacher, despite lower immediate post-distillation performance. Together, these results suggest that effective temporal self-distillation depends not simply on teacher strength, but on a balance between newly acquired capability and learner compatibility.

Scaling critic capacity is a promising direction for improving off-policy reinforcement learning (RL). However, recent work shows that larger critics are prone to overfitting and instability in replay-based bootstrapped training. In this paper, we propose using Low-Rank Adaptation (LoRA) as a structural regularizer for critic learning. Our approach freezes randomly initialized base matrices and optimizes only the corresponding low-rank adapters, thereby constraining critic updates to a low-dimensional subspace. We evaluate our method across different off-policy RL algorithms, including SAC and FastTD3 based on different network architectures. Empirically, LoRA efficiently reduces critic loss during training and improves overall policy performance, achieving the best or competitive results on most tasks. Extensive experiments demonstrate that our low-rank updates provide a simple and effective form of structural regularization for critic learning in off-policy RL.

Reinforcement Learning with Verifiable Rewards improves reasoning in large language models, yet on-policy learning often suffers from cold-start challenges in sparse-reward settings. Recent mixed-policy approaches address this by combining off-policy teacher data with on-policy training. However, simply combining these introduce a persistent off-policy gradient mass that risks training collapse and instability. To address this challenge, we propose Hindsight-Anchored Policy Optimization (HAPO), a framework that allows teacher intervention to act as a temporary support. HAPO employs Beta-Binomial confidence gating, an adaptive gating mechanism that decides when to open the gate for teacher intervention. The intervention operates with Synthetic Success Injection, which replaces the group's lowest-reward rollout with a verified teacher trajectory. We also introduce adaptive threshold annealing, which gradually retracts the support and restores on-policy training within a finite horizon to mitigate persistent off-policy drift. We demonstrate that HAPO can be layered on top of existing mixed-policy methods in a generalizable manner. Across six math reasoning benchmarks and two model scales, HAPO improves the average accuracy of three major mixed-policy methods while maintaining training stability.

Off-road autonomous driving poses significant challenges such as navigating unmapped, variable terrain with uncertain and diverse dynamics. Addressing these challenges requires effective long-horizon planning and adaptable control. Reinforcement Learning (RL) offers a promising solution by learning control policies directly from interaction. However, because off-road driving is a long-horizon task with low-signal rewards, standard RL methods are challenging to apply in this setting. We introduce TADPO, a novel policy gradient formulation that extends Proximal Policy Optimization (PPO), leveraging off-policy trajectories for teacher guidance and on-policy trajectories for student exploration. Building on this, we develop a vision-based, end-to-end RL system for high-speed off-road driving, capable of navigating extreme slopes and obstacle-rich terrain. We demonstrate our performance in simulation and, importantly, zero-shot sim-to-real transfer on a full-scale off-road vehicle. To our knowledge, this work represents the first deployment of RL-based policies on a full-scale off-road platform.

Post-training with reinforcement learning (RL) has recently shown strong promise for advancing multimodal agents beyond supervised imitation. However, RL remains limited by poor data efficiency, particularly in settings where interaction data are scarce and quickly become outdated. To address this challenge, GIPO (Gaussian Importance sampling Policy Optimization) is proposed as a policy optimization objective based on truncated importance sampling, replacing hard clipping with a log-ratio-based Gaussian trust weight to softly damp extreme importance ratios while maintaining non-zero gradients. Theoretical analysis shows that GIPO introduces an implicit, tunable constraint on the update magnitude, while concentration bounds guarantee robustness and stability under finite-sample estimation. Experimental results show that GIPO achieves state-of-the-art performance among clipping-based baselines across a wide range of replay buffer sizes, from near on-policy to highly stale data, while exhibiting superior bias--variance trade-off, high training stability and improved sample efficiency. Code is available at https://github.com/distanceLu/GIPO.

On-policy reinforcement learning (RL) for language model post-training suffers from a fundamental tension: as training progresses, policy entropy collapses and sampling diversity diminishes, causing the model to ``forget'' its own earlier exploratory capacity. While off-policy data can restore diversity, existing methods mix entire trajectories at the sequence level, introducing severe policy mismatch and training instability. We argue that the core question is not \emph{whether} to use off-policy data, but \emph{where} in the sequence it should appear. Based on this insight, we propose \textbf{Thinking Seeds}, a token-level mix-policy framework that uses the model's own historical checkpoints as off-policy prefixes, providing diverse starting points for reasoning, while the critical continuation is generated on-policy to preserve gradient quality. Through token-level importance ratios, Thinking Seeds effectively leverages historical diversity without compromising training stability. Extensive experiments across models and mathematical reasoning benchmarks demonstrate that Thinking Seeds consistently outperforms standard on-policy training and existing off-policy extensions. Our analysis reveals that the method maintains higher effective entropy, reduces gradient loss from clipping, and expands the explorable solution space, clarifying how position-aware mix-policy modeling improves both exploration and final performance in LLM RL.

Policy gradient methods for Large Language Models optimize a policy $π_θ$ via a surrogate objective computed from samples of a rollout policy $π_{\text{roll}}$. However, modern LLM-RL pipelines suffer from unavoidable implementation divergences -- backend discrepancies, Mixture-of-Experts routing discontinuities, and distributed training staleness -- causing off-policy mismatch ($π_{\text{roll}} \neq π_θ$) and approximation errors between the surrogate and the true objective. We demonstrate that classical trust region bounds on this error scale as $O(T^2)$ with sequence length $T$, rendering them vacuous for long-horizon tasks. To address this, we derive a family of bounds -- both KL-based and TV-based -- including a Pinsker-Marginal bound ($O(T^{3/2})$), a Mixed bound ($O(T)$), and an Adaptive bound that strictly generalizes the Pinsker-Marginal bound via per-position importance-ratio decomposition. Taking the minimum over all bounds yields the tightest known guarantee across all divergence regimes. Crucially, all bounds depend on the maximum token-level divergence $D_{\mathrm{KL}}^{\mathrm{tok,max}}$ (or $D_{\mathrm{TV}}^{\mathrm{tok,max}}$), a sequence-level quantity that cannot be controlled by token-independent methods like PPO clipping. We propose Trust Region Masking (TRM), which masks entire sequences violating the trust region, enabling the first non-vacuous monotonic improvement guarantees for long-horizon LLM-RL.

Reinforcement learning (RL) algorithms such as PPO and GRPO are widely used to train large language models (LLMs) for multi-turn agentic tasks. However, in off-policy training pipelines, these methods can exhibit unstable optimization dynamics and are prone to perfor- mance collapse. Through empirical analysis, we identify two fundamental sources of instability in this setting: (1) a granularity mismatch between token-level policy optimization and turn- structured interactions, and (2) high-variance and unreliable gradient updates induced by off- policy importance sampling and inaccurate advantage estimation. To address these challenges, we propose SORL, Stabilizing Off-Policy Reinforcement Learning for Long-Horizon Agent Train- ing. SORL introduces mechanisms that align policy optimization with the structure of multi- turn interactions and adaptively suppress unreliable off-policy updates, yielding more conserva- tive and robust learning dynamics. Within this framework, we instantiate two stabilized algo- rithms: SO-PPO and SO-GRPO. Both algorithms are designed to mitigate gradient variance and prevent optimization collapse without requiring careful early stopping or heuristic tuning. We evaluate SO-PPO and SO-GRPO on benchmarks spanning open-domain QA, multi-hop QA, and medical multiple-choice QA, and further assess their transfer to asynchronous RL for mathe- matical reasoning by training on DAPO-Math-17k and validating on AIME-2024. These results demonstrate that SORL provides a practical, scalable, and general framework for stabilizing re- inforcement learning in multi-turn LLM agent training and asynchronous RL for mathematical reasoning.

Off-policy reinforcement learning suffers from extrapolation errors when a learned policy selects actions that are weakly supported in the replay buffer. In this study, we address this issue by drawing an analogy to static friction. From this perspective, the replay buffer is represented as a smooth, low-dimensional action manifold, where the support directions correspond to the tangential component, while the normal component captures the dominant first-order extrapolation error. This decomposition reveals an intrinsic anisotropy in value sensitivity that naturally induces a stability condition analogous to a friction threshold. To mitigate deviations toward unsupported actions, we propose Frictional Q-Learning, an off-policy algorithm that encodes supported actions as tangent directions using a contrastive variational autoencoder. We further show that an orthonormal basis of the orthogonal complement corresponds to normal components under mild local isometry assumptions. Extensive empirical results on standard continuous-control benchmarks consistently demonstrate robust and stable performance compared with competitive baselines.

Advanced reasoning in LLMs on challenging domains like mathematical reasoning can be tackled using verifiable rewards based reinforced fine-tuning (ReFT). In standard ReFT frameworks, a behavior model generates multiple completions with answers per problem, for the answer to be then scored by a reward function. While such RL post-training methods demonstrate significant performance improvements across challenging reasoning domains, the computational cost of generating completions during training with multiple inference steps makes the training cost non-trivial. To address this, we draw inspiration from off-policy RL, and speculative decoding to introduce a novel ReFT framework, dubbed Nested-ReFT, where a subset of layers of the target model acts as the behavior model to generate off-policy completions during training. The behavior model configured with dynamic layer skipping per batch during training decreases the inference cost compared to the standard ReFT frameworks. Our theoretical analysis shows that Nested-ReFT yields unbiased gradient estimates with controlled variance. Our empirical analysis demonstrates improved computational efficiency measured as tokens/sec across multiple math reasoning benchmarks and model sizes. Additionally, we explore three variants of bias mitigation to minimize the off-policyness in the gradient updates that allows for maintaining performance that matches the baseline ReFT performance.

Proximal Policy Optimization (PPO) is a popular model-free reinforcement learning algorithm, esteemed for its simplicity and efficacy. However, due to its inherent on-policy nature, its proficiency in harnessing data from disparate policies is constrained. This paper introduces a novel off-policy extension to the original PPO method, christened Transductive Off-policy PPO (ToPPO). Herein, we provide theoretical justification for incorporating off-policy data in PPO training and prudent guidelines for its safe application. Our contribution includes a novel formulation of the policy improvement lower bound for prospective policies derived from off-policy data, accompanied by a computationally efficient mechanism to optimize this bound, underpinned by assurances of monotonic improvement. Comprehensive experimental results across six representative tasks underscore ToPPO's promising performance.

Adversarial Imitation Learning (AIL) faces challenges with sample inefficiency because of its reliance on sufficient on-policy data to evaluate the performance of the current policy during reward function updates. In this work, we study the convergence properties and sample complexity of off-policy AIL algorithms. We show that, even in the absence of importance sampling correction, reusing samples generated by the $o(\sqrt{K})$ most recent policies, where $K$ is the number of iterations of policy updates and reward updates, does not undermine the convergence guarantees of this class of algorithms. Furthermore, our results indicate that the distribution shift error induced by off-policy updates is dominated by the benefits of having more data available. This result provides theoretical support for the sample efficiency of off-policy AIL algorithms. To the best of our knowledge, this is the first work that provides theoretical guarantees for off-policy AIL algorithms.