Reinforcement Learning

Off-policy learning in constrained MDPs with large binary state spaces faces a fundamental tension: causal identification of transition dynamics requires structural assumptions, while sample-efficient policy learning requires state-space compression. We introduce PI-CMDP, a framework for CMDPs whose constraint dependencies form a layered DAG under a Lifecycle Ordering Assumption (LOA). We propose an Identify-Compress-Estimate pipeline: (i) Identify: LOA enables backdoor identification of causal edge weights for cross-layer pairs, with formal partial-identification bounds when LOA is violated; (ii) Compress: a Markov abstraction compresses state cardinality from 2^(WL) to (W+1)^L under layer-priority regularity and exchangeability; and (iii) Estimate: a physics-guided doubly-robust estimator remains unbiased and reduces the variance constant when the physics prior outperforms a learned model. We instantiate PI-CMDP on constraint repair in engineering simulation pipelines. On the TPS benchmark (4,206 episodes), PI-CMDP achieves 76.2% repair success rate with only 300 training episodes versus 70.8% for the strongest baseline (+5.4 pp), narrowing to +2.8 pp (83.4% vs. 80.6%) in the full-data regime, while substantially reducing cascade failure rates. All improvements are consistent across 5 independent seeds (paired t-test p < 0.02).

Recently, latent reasoning has been introduced into large language models (LLMs) to leverage rich information within a continuous space. However, without stochastic sampling, these methods inevitably collapse to deterministic inference, failing to discover diverse reasoning paths. To bridge the gap, we inject controllable stochasticity into latent reasoning via Gumbel-Softmax, restoring LLMs' exploratory capacity and enhancing their compatibility with Reinforcement Learning (RL). Building on this, we propose \textbf{\underline{L}}atent R\textbf{\underline{e}}asoning \textbf{\underline{P}}olicy \textbf{\underline{O}}ptimization~(\textbf{LEPO}), a novel framework that applies RL directly to continuous latent representations. Specifically, in rollout stage, LEPO maintains stochasticity to enable diverse trajectory sampling, while in optimization stage, LEPO constructs a unified gradient estimation for both latent representations and discrete tokens. Extensive experiments show that LEPO significantly outperforms existing RL methods for discrete and latent reasoning.

Exploration is a cornerstone of learning from experience: it enables agents to find solutions to complex problems, generalize to novel ones, and scale performance with test-time compute. In this paper, we present a framework for post-training language models (LMs) that explicitly encourages optimistic exploration and promotes a synergy between exploration and exploitation. The central idea is to train the LM to generate sets of responses that are collectively accurate under the reward function and exploratory in their reasoning strategies. We first develop a general recipe for optimizing LMs with set reinforcement learning (set RL) under arbitrary objective functions, showing how standard RL algorithms can be adapted to this setting through a modification to the advantage computation. We then propose Polychromic Exploratory Policy Optimization (Poly-EPO), which instantiates this framework with an objective that explicitly synergizes exploration and exploitation. Across a range of reasoning benchmarks, we show that Poly-EPO improves generalization, as evidenced by higher pass@$k$ coverage, preserves greater diversity in model generations, and effectively scales with test-time compute.

Agentic search -- the task of training agents that iteratively reason, issue queries, and synthesize retrieved information to answer complex questions -- has achieved remarkable progress through reinforcement learning (RL). However, existing approaches such as Search-R1, treat the retrieval system as a fixed tool, optimizing only the reasoning agent while the retrieval component remains unchanged. A preliminary experiment reveals that the gap between an oracle and a fixed retrieval system reaches up to +26.8% relative F1 improvement across seven QA benchmarks, suggesting that the retrieval system is a key bottleneck in scaling agentic search performance. Motivated by this finding, we propose CoSearch, a framework that jointly trains a multi-step reasoning agent and a generative document ranking model via Group Relative Policy Optimization (GRPO). To enable effective GRPO training for the ranker -- whose inputs vary across reasoning trajectories -- we introduce a semantic grouping strategy that clusters sub-queries by token-level similarity, forming valid optimization groups without additional rollouts. We further design a composite reward combining ranking quality signals with trajectory-level outcome feedback, providing the ranker with both immediate and long-term learning signals. Experiments on seven single-hop and multi-hop QA benchmarks demonstrate consistent improvements over strong baselines, with ablation studies validating each design choice. Our results show that joint training of the reasoning agent and retrieval system is both feasible and strongly performant, pointing to a key ingredient for future search agents.

Standard approaches to goal-conditioned reinforcement learning (GCRL) that rely on temporal-difference learning can be unstable and sample-inefficient due to bootstrapping. While recent work has explored contrastive and supervised formulations to improve stability, we present a probabilistic alternative, called survival value learning (SVL), that reframes GCRL as a survival learning problem by modeling the time-to-goal from each state as a probability distribution. This structured distributional Monte Carlo perspective yields a closed-form identity that expresses the goal-conditioned value function as a discounted sum of survival probabilities, enabling value estimation via a hazard model trained via maximum likelihood on both event and right-censored trajectories. We introduce three practical value estimators, including finite-horizon truncation and two binned infinite-horizon approximations to capture long-horizon objectives. Experiments on offline GCRL benchmarks show that SVL combined with hierarchical actors matches or surpasses strong hierarchical TD and Monte Carlo baselines, excelling on complex, long-horizon tasks. Webpage and Code: https://simple-robotics.github.io/publications/survival-value-learning/

Small Vision-Language Models (SVLMs) are efficient task controllers but often suffer from visual brittleness and poor tool orchestration. They typically require expensive supervised trajectory tuning to mitigate these deficits. In this work, we propose Self-supervised Perception Enabled by Cascaded Tool Rollout Alignment (SPECTRA), a supervision-free framework that bootstraps agentic capabilities via Coldstart Reinforcement Learning for SVLMs. SPECTRA enforces Soft Structured Multi-turn Rollouts, a topological constraint that directs agents to explicitly sequence tool derived evidence before synthesis, effectively grounding reasoning in visual observations. We employ a multi-objective reward signal that simultaneously maximizes task correctness, rollout structure, and tool utility, enabling agent to self-discover robust behaviors without human preference labels. We further introduce Tool Instrumental Utility (TIU), a novel metric to quantify tool efficacy in the absence of ground truth. Extensive evaluations across composite and out-of-distribution (MMMU-Pro) benchmarks demonstrate that SPECTRA boosts agentic trajectories, improving task accuracy by up to 5% and tool efficiency by 9%, enabling more efficient multimodal agents that learn effectively from environmental interaction alone.

Q-value iteration (Q-VI) is usually analyzed through the $γ$-contraction of the Bellman operator. This argument proves convergence to $Q^*$, but it gives only a coarse account of when the induced greedy policy becomes optimal. We study discounted Q-VI as a switching system and focus on the practically optimal solution set (POSS), the set of $Q$-functions whose tie-broken greedy policies are optimal. The main result shows that Q-VI reaches the optimal action class in finite time by entering an invariant tube around $\mathcal X_1=Q^*+\operatorname{span}(\mathbf 1)$, which is contained in the POSS. For every $\varepsilon>0$, the distance to $\mathcal X_1$ satisfies an exponential bound with rate $(\barρ+\varepsilon)^k$, where $\barρ$ is the joint spectral radius of the projected switching family restricted to directions transverse to $\mathcal X_1$. When $\barρ<γ$, this transverse convergence is faster than the classical contraction rate. The analysis separates fast policy identification from the subsequent convergence to $Q^*$, which may still be governed by the all-ones mode. We also give spectral and graph-theoretic conditions under which the strict inequality $\barρ<γ$ holds or fails.

This paper investigates the length problem in sequence-level relative reinforcement learning. We observe that, although existing methods partially alleviate length-related phenomena, a more fundamental issue remains insufficiently characterized: the comparison units used during training lack inherent comparability. Building on this observation, we propose a new perspective: the length problem should not be viewed merely as a loss-scaling or normalization bias, but rather as a \emph{comparison unit construction} problem. We further establish a sample-construction-based training framework that, instead of applying post-hoc corrections to unequal-length responses, proactively constructs equal-length, alignable, and comparable training segments during generation. Within this framework, we propose EqLen, a concrete method applicable to group-relative comparison algorithms such as GRPO, GSPO, and RLOO. Through dual-track synchronous generation, prefix inheritance, and segment masking, EqLen efficiently collects effective equal-length training segments and enables stable

Motivated by the challenge presented by non-Markovian objectives in reinforcement learning (RL), we present a novel framework to track and represent the progress of autonomous agents through complex, multi-stage tasks. Given a specification in finite linear temporal logic (LTL), the framework establishes a 'tracking vector' which updates at each time step in a trajectory rollout. The values of the vector represent the status of the specification as the trajectory develops, assigning true, false, or 'open' labels (where 'open' is used for indeterminate cases). Applied to an LTL formula tree, the tracking vector can be used to encode detailed information about how a task is executed over a trajectory, providing a potential tool for new performance metrics, diverse exploration, and reward shaping. In this paper, we formally present the framework and algorithm, collectively named Live LTL Progress Tracking, give a simple working example, and demonstrate avenues for its integration into RL models. Future work will apply the framework to problems such as task-space exploration and diverse solution-finding in RL.

Reinforcement learning (RL) has emerged as a promising paradigm for training reasoning-oriented models by leveraging rule-based reward signals. However, RL training typically tends to improve single-sample success rates (i.e., Pass@1) while offering limited exploration of diverse reasoning trajectories, which is crucial for multi-sample performance (i.e., Pass@k). Our preliminary analysis reveals that this limitation stems from a fundamental squeezing effect, whereby probability mass is excessively concentrated on a narrow subset of high-reward trajectories, restricting genuine exploration and constraining attainable performance under RL training. To address this issue, in this work, we propose Steering Probability Squeezing (SPS), a training paradigm that interleaves conventional RL with inverse reinforcement learning (IRL). SPS treats on-policy rollouts as demonstrations and employs IRL to explicitly reshape the induced trajectory distribution, thereby enhancing exploration without introducing external supervision. Experiments on five commonly used reasoning benchmarks demonstrate that SPS can enable better exploration and improve Pass@k. Beyond algorithmic contributions, we provide an analysis of RL learning dynamics and identify an empirical upper bound on Pass@k, shedding light on intrinsic exploration limits in RL-based reasoning models. Our findings suggest that alternating between RL and IRL offers an effective pathway toward extending the exploration capacity of reasoning-oriented large language models.

Path planning is usually solved by addressing either the (high-level) route planning problem (waypoint sequencing to achieve the final goal) or the (low-level) path planning problem (trajectory prediction between two waypoints avoiding collisions). However, real-world problems usually require simultaneous solutions to the route and path planning subproblems with a holistic and efficient approach. In this paper, we introduce NaviFormer, a deep reinforcement learning model based on a Transformer architecture that solves the global navigation problem by predicting both high-level routes and low-level trajectories. To evaluate NaviFormer, several experiments have been conducted, including comparisons with other algorithms. Results show competitive accuracy from NaviFormer since it can understand the constraints and difficulties of each subproblem and act consequently to improve performance. Moreover, its superior computation speed proves its suitability for real-time missions.

Reinforcement Learning (RL) has achieved impressive success in post-training Large Language Models (LLMs) and Vision-Language Models (VLMs), with on-policy algorithms such as PPO, GRPO, and REINFORCE++ serving as the dominant paradigm. However, these methods discard all collected trajectories after a single gradient update, resulting in poor sample efficiency, particularly wasteful for agentic tasks where multi-turn environment interactions are expensive. While Experience Replay drives sample efficiency in classic RL by allowing agents to reuse past trajectories and prioritize informative ones, directly applying Prioritized Experience Replay (PER) to LLMs fails. The rapid policy evolution of billion-parameter models renders stored priorities stale, causing old high-priority trajectories to dominate sampling long after they have become uninformative. We propose Freshness-Aware PER, which addresses this priority staleness problem by augmenting any PER-based priority with a multiplicative exponential age decay grounded in effective sample size analysis. To the best of our knowledge, Freshness-Aware PER is the first work to successfully apply PER to LLM/VLM reinforcement learning. We evaluate on eight multi-step agentic, reasoning, and math competition tasks with 0.5B, 3B, and 7B models. Freshness-Aware PER significantly outperforms on-policy baselines, achieving +46% on NQ Search, +367% on Sokoban, and +133% on VLM FrozenLake, while standard PER without age decay consistently degrades performance. Our code is publicly available at https://github.com/Vision-CAIR/Freshness-Aware-PER.

Reinforcement learning from verifiable rewards (RLVR) has demonstrated remarkable effectiveness in improving the reasoning capabilities of large language models. As models evolve into natively multimodal architectures, extending RLVR to video understanding becomes increasingly important yet remains largely unexplored, due to the diversity of video task types, the computational overhead of repeatedly decoding and preprocessing high-dimensional visual inputs, and the difficulty of reproducible evaluation across numerous sensitive hyperparameters. Existing open-source RL training frameworks provide solid infrastructure for text and image scenarios but lack systematic optimizations tailored for video modality. In this work, we present \textbf{EasyVideoR1}, a complete and efficient reinforcement learning framework specifically designed for training large vision-language models on video understanding tasks. EasyVideoR1 makes the following contributions: (1) a full video RL training pipeline with offline preprocessing and tensor caching that eliminates redundant video decoding and yields a 1.47 $\times$ throughput improvement; (2) a comprehensive, task-aware reward system covering 11 distinct video and image problem types with unified routing and modular extension; (3) a mixed offline-online data training paradigm that combines curated high-quality trajectories with on-policy exploration, benefiting the learning of more challenging tasks; (4) joint image-video training with independently configurable pixel budgets, allowing the two modalities to mutually reinforce each other; and (5) an asynchronous multi-benchmark evaluation framework covering 22 mainstream video understanding benchmarks, with reproduced accuracy closely aligned with officially reported scores.

Neuro-symbolic Reinforcement Learning (NeSy-RL) combines symbolic reasoning with gradient-based optimization to achieve interpretable and generalizable policies. Relational concepts, such as "left of" or "close by", serve as foundational building blocks that structure how agents perceive and act. However, conventional approaches require human experts to manually define these concepts, limiting adaptability since concept semantics vary across environments. We propose GRAIL (Grounding Relational Agents through Interactive Learning), a framework that autonomously grounds relational concepts through environmental interaction. GRAIL leverages large language models (LLMs) to provide generic concept representations as weak supervision, then refines them to capture environment-specific semantics. This approach addresses both sparse reward signals and concept misalignment prevalent in underdetermined environments. Experiments on the Atari games Kangaroo, Seaquest, and Skiing demonstrate that GRAIL matches or outperforms agents with manually crafted concepts in simplified settings, and reveals informative trade-offs between reward maximization and high-level goal completion in the full environment.

Frontier models have demonstrated exceptional capabilities following the integration of task-reward-based reinforcement learning (RL) into their training pipelines, enabling systems to evolve from pure reasoning models into sophisticated agents. However, debate persists regarding whether RL genuinely instills new skills within a base model or merely sharpens its existing distribution to elicit latent capabilities. To address this dichotomy, we present an explicit comparison between distribution sharpening and task-reward-based learning, utilizing RL as a tool to implement both paradigms. Our analysis reveals the inherent limitations of distribution sharpening, demonstrating from first principles how and why the optima can be unfavorable and the approach fundamentally unstable. Furthermore, our experiments using Llama-3.2-3B-Instruct, Qwen2.5-3B-Instruct and Qwen3-4B-Instruct-2507 on math datasets confirm that sharpening yields limited gains, whereas incorporating task-based reward signal can greatly help achieve robust performance improvements and stable learning.

This research note identifies a previously overlooked distinction between multi-objective reinforcement learning (MORL), and more conventional single-objective reinforcement learning (RL). It has previously been noted that the optimal policy for an MORL agent with a non-linear utility function is required to be conditioned on both the current environmental state and on some measure of the previously accrued reward. This is generally implemented by concatenating the observed state of the environment with the discounted sum of previous rewards to create an augmented state. While augmented states have been widely-used in the MORL literature, one implication of their use has not previously been reported -- namely that they require the agent to have continued access to the reward signal (or a proxy thereof) after deployment, even if no further learning is required. This note explains why this is the case, and considers the practical repercussions of this requirement.

This paper proposes a novel method that incorporates empowerment when reasoning actions in reinforcement learning (RL), thereby achieving the flexibility of exploration-exploitation dilemma (EED). In previous methods, empowerment for promoting exploration has been provided as a bonus term to the task-specific reward function as an intrinsically-motivated RL. However, this approach introduces a delay until the policy that accounts for empowerment is learned, making it difficult to adjust the emphasis on exploration as needed. On the other hand, a trick devised for fine-tuning recent foundation models at reasoning, so-called best-of-N (BoN) sampling, allows for the implicit acquisition of modified policies without explicitly learning them. It is expected that applying this trick to exploration-promoting terms, such as empowerment, will enable more flexible adjustment of EED. Therefore, this paper investigates BoN sampling for empowerment. Furthermore, to adjust the degree of policy modification in a generalizable manner while maintaining computational cost, this paper proposes a novel BoN sampling method extended by Tsalis statistics. Through toy problems, the proposed method's cability to balance EED is verified. In addition, it is demonstrated that the proposed method improves RL performance to solve complex locomotion tasks.

Reinforcement learning is a promising approach to autonomous and adaptive security management in networked systems. However, current reinforcement learning solutions for security management are mostly limited to simulation environments and it is unclear how they generalize to operational systems. In this paper, we address this limitation by presenting CSLE: a reinforcement learning platform for autonomous security management that enables experimentation under realistic conditions. Conceptually, CSLE encompasses two systems. First, it includes an emulation system that replicates key components of the target system in a virtualized environment. We use this system to gather measurements and logs, based on which we identify a system model, such as a Markov decision process. Second, it includes a simulation system where security strategies are efficiently learned through simulations of the system model. The learned strategies are then evaluated and refined in the emulation system to close the gap between theoretical and operational performance. We demonstrate CSLE through four use cases: flow control, replication control, segmentation control, and recovery control. Through these use cases, we show that CSLE enables near-optimal security management in an environment that approximates an operational system.

Continual reinforcement learning must balance retention with adaptation, yet many methods still rely on \emph{single-model preservation}, committing to one evolving policy as the main reusable solution across tasks. Even when a previously successful policy is retained, it may no longer provide a reliable starting point for rapid adaptation after interference, reflecting a form of \emph{loss of plasticity} that single-policy preservation cannot address. Inspired by quality-diversity methods, we introduce \textsc{TeLAPA} (Transfer-Enabled Latent-Aligned Policy Archives), a continual RL framework that organizes behaviorally diverse policy neighborhoods into per-task archives and maintains a shared latent space so that archived policies remain comparable and reusable under non-stationary drift. This perspective shifts continual RL from retaining isolated solutions to maintaining \emph{skill-aligned neighborhoods} with competent and behaviorally related policies that support future relearning. In our MiniGrid CL setting, \textsc{TeLAPA} learns more tasks successfully, recovers competence faster on revisited tasks after interference, and retains higher performance across a sequence of tasks. Our analyses show that source-optimal policies are often not transfer-optimal, even within a local competent neighborhood, and that effective reuse depends on retaining and selecting among multiple nearby alternatives rather than collapsing them to one representative. Together, these results reframe continual RL around reusable and competent policy neighborhoods, providing a route beyond single-model preservation toward more plastic lifelong agents.

Reinforcement Learning (RL) has emerged as a critical driver for enhancing the reasoning capabilities of Large Language Models (LLMs). While recent advancements have focused on reward engineering or data synthesis, few studies exploit the model's intrinsic representation characteristics to guide the training process. In this paper, we first observe the presence of high-magnitude activations within the query and key vectors when processing long contexts. Drawing inspiration from model quantization -- which establishes the criticality of such high-magnitude activations -- and the insight that long-context reasoning inherently exhibits a sparse structure, we hypothesize that these weights serve as the pivotal drivers for effective model optimization. Based on this insight, we propose LongAct, a strategy that shifts from uniform to saliency-guided sparse updates. By selectively updating only the weights associated with these significant activations, LongAct achieves an approximate 8% improvement on LongBench v2 and enhances generalization on the RULER benchmark. Furthermore, our method exhibits remarkable universality, consistently boosting performance across diverse RL algorithms such as GRPO and DAPO. Extensive ablation studies suggest that focusing on these salient features is key to unlocking long-context potential.

We present a geometric framework for Reinforcement Learning (RL) that views policies as maps into the Wasserstein space of action probabilities. First, we define a Riemannian structure induced by stationary distributions, providing rigorous guarantees for their existence in a general context. We then define the tangent space of policies and characterize the geodesics, specifically addressing the measurability of vector fields mapping from the state space to the tangent space of probability measures over the action space. Next, we formulate a general RL optimization problem and construct a gradient flow using Otto's calculus. We compute the gradient and the Hessian of the energy (i.e., the expected cumulative cost), providing a formal second-order analysis. Finally, we illustrate the method with numerical examples: we compute the gradient directly from our theoretical formalism for low-dimensional problems, and we illustrate the numerical applicability of our formal framework to high-dimensional continuous control by parameterizing the policy with a neural network optimized via an ergodic approximation of the cost.

Recent advances in reinforcement learning (RL) have improved the reasoning capabilities of large language models (LLMs) and vision-language models (VLMs). However, the widely used Group Relative Policy Optimization (GRPO) consistently suffers from entropy collapse, causing the policy to converge prematurely and lose diversity. Existing exploration methods introduce additional bias or variance during exploration, making it difficult to maintain optimization stability. We propose Unified Entropy Control for Reinforcement Learning (UEC-RL), a framework that provides targeted mechanisms for exploration and stabilization. UEC-RL activates more exploration on difficult prompts to search for potential and valuable reasoning trajectories. In parallel, a stabilizer prevents entropy from growing uncontrollably, thereby keeping training stable as the model consolidates reliable behaviors. Together, these components expand the search space when needed while maintaining robust optimization throughout training. Experiments on both LLM and VLM reasoning tasks show consistent gains over RL baselines on both Pass@1 and Pass@$k$. On Geometry3K, UEC-RL achieves a 37.9% relative improvement over GRPO, indicating that it sustains effective exploration without compromising convergence and underscoring UEC-RL as a key for scaling RL-based reasoning in large models. Our code is available at https://github.com/597358816/UEC-RL.

Artificial intelligence (AI) is moving increasingly beyond prediction to support decisions in complex, uncertain, and dynamic environments. This shift creates a natural intersection with operations research and management science (OR/MS), which has long provided methodological foundations for sequential decision making under uncertainty. At the same time, deep learning advances, including feedforward neural networks, recurrent architectures, transformers, large language models (LLMs), and deep reinforcement learning, have expanded data-driven modeling for large-scale decisions. This tutorial presents an OR/MS-centered perspective on deep learning for sequential decision making under uncertainty, bridging neural architectures and OR/MS approaches to decision making. Its premise: deep learning complements optimization rather than replacing it. Deep learning brings adaptability and scalable approximation, whereas OR/MS provides the mathematical rigor to represent constraints, recourse, uncertainty, and decision quality. The tutorial reviews key decision making foundations, connects them to the major neural architectures in modern AI, and organizes the field around three central themes: predict-then-optimize and decision-aware learning, learning-based decision generation under constraints for continuous and discrete problems with temporal coupling, and deep reinforcement learning for sequential and combinatorial decision making. Impact spans supply chains, service systems, healthcare and epidemic response, agriculture, energy, environmental sustainability, and autonomous operations. This tutorial frames these developments as part of a shift from predictive AI toward decision-capable AI, highlighting OR/MS's role in shaping the next generation of integrated learning--optimization systems.

Large language models are increasingly deployed in high-stakes domains, where confident yet incorrect inferences may cause severe real-world harm, bringing the long-overlooked issue of confidence faithfulness to the forefront. A promising solution jointly optimizes unsupervised Reinforcement Learning from Internal Feedback (RLIF) with reasoning-trace-guided Reasoning Distillation (RD), yet it faces three persistent challenges, namely the scarcity of high-quality training corpora, factually unwarranted overconfidence, and erroneous updates amplified by indiscriminate fusion. Inspired by how human confidence accumulates from uncertainty to certainty, we propose Progressive Reasoning Gain (PRG) to measure whether reasoning steps progressively strengthen confidence in the final answer. Building on PRG, we introduce HyTuning, a hybrid post-training framework that adaptively reweights RD and RLIF, using scarce supervised reasoning traces as a stable anchor while exploiting abundant unlabeled queries for scalability. Experiments on several domain-specific and general benchmarks demonstrate that HyTuning improves accuracy while achieving confidence faithfulness under limited supervision, supporting a practical ``Less Data Approximates More'' effect. Our code will be released upon acceptance.

As the demand for mobile robots continues to increase, social navigation has emerged as a critical task, driving active research into deep reinforcement learning (RL) approaches. However, because pedestrian dynamics and social conventions vary widely across different regions, simulations cannot easily encompass all possible real-world scenarios. Real-world RL, in which agents learn while operating directly in physical environments, presents a promising solution to this issue. Nevertheless, this approach faces significant challenges, particularly regarding constrained computational resources on edge devices and learning efficiency. In this study, we propose incremental residual RL (IRRL). This method integrates incremental learning, which is a lightweight process that operates without a replay buffer or batch updates, with residual RL, which enhances learning efficiency by training only on the residuals relative to a base policy. Through the simulation experiments, we demonstrated that, despite lacking a replay buffer, IRRL achieved performance comparable to those of conventional replay buffer-based methods and outperformed existing incremental learning approaches. Furthermore, the real-world experiments confirmed that IRRL can enable robots to effectively adapt to previously unseen environments through the real-world learning.

We present ReBound (reset-aware semi-Markov bootstrapping), a value-learning method for reset-free reinforcement learning (RL) that learns agile driving through real-world RL without human intervention after training starts. Reset-free RL explores by alternating between a forward policy that performs the task and a reset policy that restores a drivable state. Standard reset-free RL treats collisions as episode terminations in value-function bootstrapping, truncating the return at each collision. This conflicts with the reset-free objective, under which driving resumes after recovery, and acts as a hidden collision penalty absent from the reward function. ReBound instead applies semi-Markov bootstrapping: it treats the collision-causing action and the subsequent recovery as a single semi-Markov transition and bootstraps from the post-recovery value, discounted by the actual recovery time. We further apply reward centering to stabilize value learning in the resulting continuing task. In simulation and on a 1/10-scale vehicle, ReBound substantially outperforms conventional value-learning methods and model-based control.

Reinforcement Learning with Verifiable Rewards (RLVR) is widely used for post-training Large Language Models, but practical verifiers can make errors. We study how the rate and structure of reward noise affect RLVR in code generation, with a preliminary scientific-reasoning check. In multi-seed Qwen3 8B experiments on MBPP, mean validation reward over two fixed late evaluations is within 1 percentage point of the clean baseline at the tested resampled group-rollout noise rates through 20%, and within about 2 points at 30%. Confidence intervals allow larger losses; these point estimates do not establish a general tolerance threshold. We also examine full-program pass@k, four controlled noise structures, two model-based verifiers, and policy models from three families spanning 4B-9B parameters. We derive conditional advantage distributions for symmetric and asymmetric group noise, including retained format penalties, and show why clipping limits simple gradient-scaling arguments. The analysis identifies information preserved by whole-group corruption and limits on interpreting our asymmetric sweep as a precision-recall comparison. Overall, the results indicate that imperfect verification can support effective RLVR in the tested settings, while aggregate error rates alone do not characterize the learning signal.

Value iteration-type methods have been extensively studied for computing a nearly optimal value function in reinforcement learning (RL). Under a generative sampling model, these methods can achieve sharper sample complexity than policy optimization approaches, particularly in their dependence on the discount factor. In practice, they are often employed for offline training. In this paper, we consider discounted Markov decision processes with state space S, action space A, discount factor $γ\in(0,1)$ and costs in $[0,1]$. We introduce a novel value optimization method, termed value mirror descent (VMD), which integrates mirror descent from convex optimization into the classical value iteration framework. In the deterministic setting with known transition kernels, we show that VMD converges linearly. For the stochastic setting with a generative model, we develop a stochastic variant, SVMD, which incorporates variance reduction commonly used in stochastic value iteration-type methods. For RL problems with general convex regularizers, SVMD attains a near-optimal sample complexity of $\tilde{O}(|S||A|(1-γ)^{-3}ε^{-2})$. Moreover, we establish that the Bregman divergence between the generated and optimal policies remains bounded throughout the iterations, even under the presence of model misspecification. This property is absent in existing stochastic value iteration-type methods but is important for enabling effective online (continual) learning following offline training. Under a strongly convex regularizer, SVMD achieves sample complexity of $\tilde{O}(|S||A|(1-γ)^{-5}ε^{-1})$, improving performance in the high-accuracy regime. Furthermore, we prove convergence of the generated policy to the optimal policy. Overall, the proposed method, its analysis, and the resulting guarantees, constitute new contributions to the RL and optimization literature.

Rerankers play a pivotal role in refining retrieval results for Retrieval-Augmented Generation. However, current reranking models are typically optimized on static human annotated relevance labels in isolation, decoupled from the downstream generation process. This isolation leads to a fundamental misalignment: documents identified as topically relevant by information retrieval metrics often fail to provide the actual utility required by the LLM for precise answer generation. To bridge this gap, we introduce ReRanking Preference Optimization (RRPO), a reinforcement learning framework that directly aligns reranking with the LLM's generation quality. By formulating reranking as a sequential decision-making process, RRPO optimizes for context utility using LLM feedback, thereby eliminating the need for expensive human annotations. To ensure training stability, we further introduce a reference-anchored deterministic baseline. Extensive experiments on knowledge-intensive benchmarks demonstrate that RRPO significantly outperforms strong baselines, including the powerful list-wise reranker RankZephyr. Further analysis highlights the versatility of our framework: it generalizes seamlessly to diverse readers (e.g., GPT-4o), integrates orthogonally with query expansion modules like Query2Doc, and remains robust even when trained with noisy supervisors.

Reinforcement learning has shown strong performance in robotic manipulation, but learned policies often degrade in performance when test conditions differ from the training distribution. This limitation is especially important for reliable robot planning and control in contact-rich tasks such as pushing and pick-and-place, where changes in goals, contact conditions, or robot dynamics can drive the system out-of-distribution at inference time. In this paper, we investigate a hybrid controller that combines reinforcement learning with bounded extremum seeking (ES) to improve robustness under such conditions. In the proposed approach, deep deterministic policy gradient (DDPG) policies are trained under standard conditions on the robotic pushing and pick-and-place tasks, and are then combined with bounded ES during deployment. The RL policy provides fast manipulation behavior, while bounded ES ensures robustness of the overall controller to time variations when operating conditions depart from those seen during training. The resulting controller is evaluated under several out-of-distribution settings, including time-varying goals and spatially varying friction patches. Crucially, under reasonable assumptions, we prove finite time RL-based convergence of a robotic arm to an object after which bounded ES achieves finite-time convergence to a bounded velocity moving target. We provide analytic formulas for both convergence times, and an ability to tune the convergence times by our choice of gains.