Reinforcement Learning

Reinforcement learning with verifiable rewards (RLVR), due to the deterministic verification, becomes a dominant paradigm for enhancing the reasoning ability of large language models (LLMs). The community witnesses the rapid change from the Proximal Policy Optimization (PPO) to Group Relative Policy Optimization (GRPO), in which GRPO reduces the complicated advantage estimation with simple estimation over grouped positive and negative rollouts. However, we note that negative rollouts may admit no gradation of failure severity, and the combinatorial vastness makes penalizing a few sampled negatives unlikely to cover a meaningful reward signal under sparse binary rewards. In this work, we propose Positive-Only Policy Optimization (POPO), a novel RLVR framework in which learning can occur exclusively via online positive rollouts. Specifically, POPO utilizes bounded importance sampling over the positive rollout set. Thus, no disjoint negative rollouts are used for the gradient guidance. We show that implicit negative gradients can emerge naturally through reinforcing the positive probability via rollouts redistribution. Next, POPO stabilizes the policy optimization through two mechanisms. First, it applies a siamese policy network with a momentum-based adaptation law for stabilized policy evolution. Second, we replace the KL-divergence with a bounded similarity penalty term in the siamese representation space. We conduct extensive experiments using publicly available, well-established text-LLM models, e.g., the Qwen family, across all-level mathematical benchmarks. Our experiment demonstrates that POPO achieves performance comparable to, or even superior to GRPO. Notably, we show that POPO can achieve 36.67% in AIME 2025 with Qwen-Math-7B, outperforming GRPO 30.00%. Our ablation and sweep studies further illustrate the necessity and robustness of POPO components.

Learning from a sequence of interactions, as soon as observations are perceived and acted upon, without explicitly storing them, holds the promise of simpler, more efficient and adaptive algorithms. For over a decade, however, deep reinforcement learning walked the contrary path, augmenting agents with replay buffers or parallel sampling routines, in an effort to tame learning instability. Recently, this topic has been revisited by Elsayed et al. (2024), focusing on update computation through eligibility traces and modifications to the optimisation routine, resulting in the StreamQ algorithm. In this work we take a step back, investigating the efficacy of established updates, such as those implemented by DQN and C51 within this online setting. Not only do we find that they perform well, but through analysing how the optimisation algorithm generally, and Adam in particular, interacts with these updates, we contend that two properties are essential for robust performance: i) the derivative of the objective is to be bounded and ii) weight updates are variance-adjusted. Rigorous and exhaustive experimentation demonstrates that C51, which exhibits both characteristics, is competitive with StreamQ across a subset of 55 Atari games. Using these insights, we derive a variance-adjusted algorithm based on eligibility traces, termed Adaptive Q$(λ)$, which approaches double the human baseline on the same subset, surpassing existing methods by all performance metrics.

The design of biological systems is hindered by uncertainty arising from both intrinsic stochasticity of biomolecular reactions and variability across laboratory or experimental conditions. In this work, we present a sequential framework to optimize genetic circuits under both forms of uncertainty. By employing simulator models based on differential equations or Markov jump processes alongside a reinforcement learning (RL) policy-based approach, our method suggests experiments that adapt to unknown laboratory conditions while accounting for inherent stochasticity. While previous Bayesian methods address uncertainty through iterative experiment-inference-optimization cycles, they typically require computationally expensive inference and optimization steps after each experimental round, leading to delays. To overcome this bottleneck, we propose an amortized approach trained up-front across a distribution of possible uncertain parameters. This strategy sidesteps the need for explicit parameter inference during the design cycle, enabling immediate, observation-based adaptation. We demonstrate our framework on models for heterologous gene expression and a repressilator circuit, showing that it efficiently handles both molecular noise and cross-laboratory variability.

Outcome metrics can certify the wrong behavior. We study this failure in a two-hotel revenue-management simulator where Hotel A trains an agent against a fixed rule-based revenue-management competitor, Hotel B. A standard learning agent can obtain near-reference revenue per available room (RevPAR) while failing to learn market-like yield management: it sells too aggressively, undercuts, or collapses to modal price buckets. We diagnose this as a Goodhart-style failure under partial observability. Hotel A cannot observe the competitor's remaining inventory, booking curve, or pricing rule, so the same Hotel A-visible state maps to multiple plausible Hotel B prices. Deterministic value-based RL and deterministic copying collapse this unresolved uncertainty into shortcut behavior. We introduce a trace-level diagnostic protocol using RevPAR, occupancy, ADR, full price-bucket distributions, L1/JS distances, and seed-level confidence intervals. The verified repair is Trace-Prior RL: learn a distributional market prior from lagged market traces, then train a stochastic pricing policy with a RevPAR reward and a KL penalty to the learned prior. The final policy matches Hotel B's RevPAR, occupancy, ADR, and price distribution within seed-level uncertainty, while still optimizing Hotel A's own reward. We argue that the contribution is not a new optimizer and not a hotel-pricing leaderboard, but a reproducible failure-and-repair recipe for agentic systems where scalar rewards are easy to game and the intended behavior is only visible in traces. A key finding is that higher exact action accuracy can worsen aggregate trace alignment when the target is distributional.

Recent extensive research has demonstrated that the enhanced reasoning capabilities acquired by models through Reinforcement Learning with Verifiable Rewards (RLVR) are primarily concentrated within the rank-1 components. Predicated on this observation, we employed Periodic Rank-1 Substitution and identified a counterintuitive phenomenon: RLVR may exhibit implicit reward overfitting to the training dataset. Specifically, the model can achieve satisfactory performance on the test set even when its rewards remain relatively low during the training process. Furthermore, we characterize three distinct properties of RL training: (1) The effective rank-1 component in RLVR don't maintain other model knowledge except mathematical reasoning capability. (2) RLVR fundamentally functions by optimizing a specific singular spectrum. The distribution of singular values of almost all linear layers in RLVR-trained model behaves like heavy-tailed distribution. (3) the left singular vectors associated with rank-1 components demonstrate a stronger alignment tendency during training, which echoes the discovery that RLVR is optimizing sampling efficiency in essence. Taken together, our findings and analysis further reveal how RLVR shapes model parameters and offer potential insights for improving existing RL paradigms or other training paradigms to implement continual learning.

Reinforcement learning (RL) with continuous time and state/action spaces is often data-intensive and brittle under nuisance variability and shift, motivating methods that exploit value-preserving structures to stabilize and improve learning. Most existing approaches focus on special cases, such as prescribed symmetries and exact equivariance, without addressing how to discover more general structures that require nonlinear operators to transform and map between continuous state/action systems with isomorphic value functions. We propose \textbf{VPSD-RL} (Value-Preserving Structure Discovery for Reinforcement Learning). It models continuous RL as a controlled diffusion with value-preserving mappings defined through Lie-group actions and associated pullback operators. We show that a value-preserving structure exists exactly when pulling back the value function and pushing forward actions commute with the controlled generator and reward functional. Further, approximate value-preserving structures with rigorous guarantees can be found when the Hamilton--Jacobi--Bellman mismatch is small. This framework discovers exact and approximate value-preserving structures by searching for the associated Lie group operators. VPSD-RL fits differentiable drift, diffusion, and reward models; learns infinitesimal generators via determining-equation residual minimization; exponentiates them with ODE flows to obtain finite transformations; and integrates them into continuous RL through transition augmentation and transformation-consistency regularization. We show that bounded generator/reward mismatch implies quantitative stability of the optimal value function along approximate orbits, with sensitivity governed by the effective horizon, and observe improved data efficiency and robustness on continuous-control benchmarks.

A hallmark of life on Earth is the ability of agents to exert causal power and be drivers of subsequent events. This is key to cognition at all scales. Causal emergence, measuring the degree to which an agent exerts unique predictive power on its future, is one consequence of causal power. Indeed, recent discoveries have shown that biological agents, even minimal ones, increase their causal emergence after learning new memories. However, there is a major knowledge gap regarding how causally emergent artificial agents are. We focused on Reinforcement Learning (RL) of neural-network agents across an array of environmental conditions, encompassing different algorithms, agent architectures, and six environments arranged on a complexity spectrum. For consistency, we computed the causal emergence of their latent-space representations over their lifetimes. We used the recently proposed ΦID to estimate causal emergence and tested how it related to learning performance. Our results suggested a Causally Emergent Alignment Hypothesis: successful agents exhibited causal emergence that was consistently predictive of final reward early in training and whose representational dynamics aligned with reward improvement in most tasks. This idea suggests that causal emergence may be a previously undisclosed axis of reorganization of neural representations in RL agents, with the potential to establish causal relationships and interventions that will lead to better RL agents. Our work also highlights the alignment between causal emergence and learning as another way biological and artificial creatures compare.

Finite-sample analyses of deep Q-learning typically treat replayed data as independent, even though it is sampled from temporally dependent state-action trajectories. We study the Deep Q-networks (DQN) algorithm under explicit dependence by modelling the minibatches used for updating the network as $τ$-mixing. We show that this assumption holds under certain dependence conditions on the underlying trajectories and the mechanism used to sample minibatches. Building on this observation, we extend statistical analyses of DQN with fully connected ReLU architectures to dependent data. We formulate each update as a nonparametric regression problem with $τ$-mixing observations and derive finite-sample risk bounds under this dependence structure. Our results show that temporal dependence leads to a degradation in the statistical rate by inducing an additional dimensionality penalty in the rate exponent, reflecting the reduced effective sample size of $τ$-mixing data. Moreover, we derive the sample complexity of DQN under $tau$-mixing from these risk bounds. Finally, we empirically demonstrate on standard Gymnasium environments that the independence assumption is systematically violated and that replay sampling yields approximately exponentially decaying correlations, supporting our theoretical framework.

State-of-the-art model-based reinforcement learning methods train policies on imagined rollouts. These rollouts are trajectories generated by a learned dynamics model and are scored by a learned reward model, but without querying the true environment during policy updates. We study this training paradigm by quantifying how errors in learned dynamics and reward models affect returns and policy optimization. First, we extend the analysis of Asadi et al. (2018) to MDPs with learned reward models, and derive the optimal sample allocation--the ratio of dynamics samples to reward samples that minimizes a bound on return error under power-law scaling assumptions. We identify lower Lipschitz constants of the learned dynamics, reward, and policy as a representation desideratum that tightens this bound, and we connect this perspective to the temporal-straightening objective of Wang et al. (2026). Second, we examine how policy optimization with REINFORCE tolerates noisy rewards, which are often cheaper to obtain. We show that zero-mean reward noise leaves the gradient estimator unbiased and adds at most a variance term that decreases with the number of rollouts. This introduces a practical tradeoff: given a fixed budget, should one buy more rollouts with cheaper but noisier rewards, or fewer rollouts with more expensive but less noisy rewards? We reduce this choice to a one-dimensional optimization problem and characterize the optimum.

The discount factor in reinforcement learning controls both the effective planning horizon and the strength of bootstrapping, yet most deep RL methods use a single fixed value across all states. While state-dependent discounting is conceptually appealing, naive deep actor--critic implementations can become unstable and degenerate toward TD-error collapse. We propose AdaGamma, a practical deep actor--critic method for state-dependent discounting that learns a state-dependent discount function together with a return-consistency objective to regularize the induced backup structure. On the theory side, we analyze the Bellman operator induced by state-dependent discounting and establish its basic well-posedness properties under suitable conditions. Empirically, AdaGamma integrates into both SAC and PPO, yielding consistent improvements on continuous-control benchmarks, and achieves statistically significant gains in an online A/B test on the JD Logistics platform. These results suggest that state-dependent discounting can be made effective in deep RL when coupled with a return-consistency objective that prevents degenerate target manipulation.

Unsupervised pretraining has driven empirical advances in goal-conditioned reinforcement learning (GCRL), but its theoretical foundations remain poorly understood. In particular, an influential class of methods, mutual information skill learning (MISL), discovers behaviorally diverse skills that can later be used for downstream goal-reaching. However, it remains a theoretical mystery why skills learned through MISL should support goal-reaching. A subtle challenge is that both GCRL and MISL are umbrella terms: different GCRL tasks use distinct criteria for measuring goal-reaching performance, while different MISL methods optimize distinct notions of behavioral diversity. We address this challenge and unify GCRL and MISL as instances of control maximization. We identify three canonical GCRL formulations and prove that they are fundamentally inequivalent: they can induce incompatible optimal policies even in the same environment. Nevertheless, they all share a common interpretation: a well-performing goal-conditioned policy is one whose future trajectory is highly sensitive to the commanded goal, with the precise notion of sensitivity determined by the GCRL formulation. Noting that MISL objectives can be understood as measures of skill-sensitivity akin to goal-sensitivity, we show that MISL objectives are bounded by formulation-specific downstream goal-sensitivities. These bounds establish a precise correspondence between MISL methods and downstream GCRL tasks: for every GCRL formulation, there exists a matching MISL objective for which more diverse skills afford greater downstream goal sensitivity. Our results thus lay a theoretical foundation for RL pretraining and have important practical implications, such as suggesting which pretraining objectives to use when a user cares about a specific class of downstream tasks.

Reinforcement learning (RL) with verifiable rewards has proven effective at post-training LLMs for coding, yet deploying separate task-specific specialists incurs costs that scale with the number of tasks, motivating a unified multi-task RL (MTRL) approach. However, existing MTRL methods treat all coding tasks uniformly, relying on fixed data curricula under a shared optimization strategy, ultimately limiting the effectiveness of multi-task training. To address these limitations, we propose ASTOR, a multi-tASk code reinforcement learning framework via uTility-driven coORdination. Centered on task utility, a signal capturing each task learning potential and cross-task synergy, ASTOR comprises two coupled modules: 1) Hierarchical Utility-Routed Data Scheduling module hierarchically allocates training budget and prioritizes informative prompts, steering training toward the most valuable data and 2) Adaptive Utility-Calibrated Policy Optimization module dynamically scales per-task KL regularization, matching update constraints to each tasks current training state. Experiments on two widely-used LLMs across four representative coding tasks demonstrate that ASTOR consistently improves a single model across all tasks, outperforming the best task-specific specialist by 9.0%-9.5% and surpassing the strongest MTRL baseline by 7.5%-12.8%.

Decision Transformer (DT) formulates offline reinforcement learning as autoregressive sequence modeling, achieving promising results by predicting actions from a sequence of Return-to-Go (RTG), state, and action tokens. However, RTG is a scalar that summarizes future rewards, containing far less information than typical state or action vectors, yet it consumes the same computational budget per token. Worse, the self-attention cost of Transformers grows quadratically with sequence length, so including RTG as a separate token adds unnecessary overhead. We propose SlimDT, which removes RTG from the autoregressive sequence. Instead, we inject RTG information into the state representations before the sequential modeling step, allowing the Transformer to process only a compact (state, action) sequence. This reduces the sequence length by one-third, directly improving inference efficiency. On the D4RL benchmark, SlimDT surpasses standard DT across various tasks and achieves performance comparable to existing state-of-the-art methods. Decoupling a sparse conditioning signal from an information-rich sequence thus yields both computational gains and higher task performance.

Causal reinforcement learning (RL) lacks benchmarks for complex systems that combine sequential decision making, hidden information, large masked action spaces, and explicit causal structure. We introduce MTG-Causal-RL, a Gymnasium benchmark built on Magic: The Gathering with a 3,077-dimensional partial observation, a 478-action masked discrete action space, five competitive Standard archetypes, three reward schemes, and a hand-specified Structural Causal Model (SCM) over strategic variables. Every episode exposes causal variables, SCM-predicted intervention effects, and per-factor credit traces, making causal credit assignment, leave-one-out cross-archetype transfer, and policy auditability first-class metrics. We adapt a panel of reference baselines: random, heuristic, masked PPO, a causal-world-model PPO variant, and an architecture-matched scalar control. We propose Causal Graph-Factored Advantage PPO (CGFA-PPO) as a reference causal agent that uses SCM parents of win probability as factor-aligned critic targets with an intervention-calibration loss. All comparisons use paired seeds, paired-bootstrap confidence intervals, and Holm-Bonferroni correction within pre-registered families. Masked PPO and CGFA-PPO reach competitive in-distribution win rates and exceed the random baseline; per-factor calibration trajectories and leave-one-out transfer gaps expose diagnostic structure that scalar win rate alone cannot. We release the benchmark, reference-baseline results, and full evaluation protocol openly. By coupling a strategically rich, partially observed domain with an explicit causal interface and statistical protocol, MTG-Causal-RL gives causal-RL, world-model, and LLM-agent research a shared testbed for questions current benchmarks cannot pose together: causal credit assignment under masked action spaces, structural transfer across archetypes, and SCM-grounded policy auditability.

Measuring learning progress is essential for curiosity-driven exploration in reinforcement learning, but widely used signals such as prediction error often fail to distinguish meaningful, learnable patterns from random noise. This paper proposes Gradient-Momentum Coupling (GMC), a signal derived from optimization dynamics that quantifies how useful each sample's gradient is for ongoing learning by measuring its per-parameter normalized absolute product with the momentum from previous gradients. By leveraging momentum's natural filtering of noise and oscillations, GMC identifies samples that contribute to ongoing parameter updates. Controlled experiments demonstrate noise robustness and emergent curriculum learning, with the signal prioritizing tasks by learning speed rather than difficulty. Experiments on MiniGrid suggest that replacing prediction error with GMC within existing curiosity-driven architectures can improve robustness to observation noise.

Group-relative RL training (GRPO) samples a small group of parallel rollouts for every training prompt and uses their within-group reward spread to compute per-trajectory advantages. In agentic environments each rollout is a long multi-turn dialogue with one LLM call per step, so this multi-sample multiplier dominates the total training cost. When every rollout of a prompt ends with the same reward, the group has zero reward variance and contributes no gradient, so the extra rollouts add no information; such groups are common in practice (typically around 40% of all groups), so the wasted-compute fraction is substantial rather than marginal. Existing methods filter such groups at the prompt level, either after their rollouts are paid for or before any rollout begins, but both decide without using information that becomes available during the rollout itself. We instead ask whether the in-group divergence between the partial trajectories at an intermediate step can already predict that the group will be zero-variance: when the parallel rollouts have already converged on the same action prefix, the group is on track to produce a single reward, and we can stop early. We propose a one-parameter gate that stops a group when the mean pairwise prefix edit distance between its partial action sequences falls below a threshold. On a 60-iteration on-policy GRPO run on ALFWorld with Qwen2.5-7B, averaged over four random seeds, the gated arm finishes 10.7% faster in wall-clock (bootstrap 95% CI excludes 0) and shifts held-out success rate on 50 unseen tasks by +2.5 pp, with the held-out gain tracing to a measurable reduction in zero-advantage gradient-batch dilution. Code is available at https://github.com/zhiyuanZhai20/selective-rollout.

Decomposing complex tasks into a sequence of simpler subtasks can improve learning efficiency for an autonomous agent. Reinforcement learning (RL) can be used to optimize agent policies to complete subtasks, but requires well-defined subtask rewards and benefits from action masking. Recent work uses large language models (LLMs) to automate reward shaping and action masking, however none of them fully address reactivity to subtask failure and modularity to varying objects for compositional tasks. To overcome these challenges, we develop masking reward behavior tree (MRBT), a symbolic structure used as a reactive and modular reward and action mask function. We design an MRBT template and derive logical specifications to construct and verify MRBTs for a sequence of object-interaction subtasks. Further, we develop an automated pipeline that uses an LLM to generate MRBTs robust to varying task objects, an SMT-solver to verify correctness of specifications, and a neurosymbolic RL loop to train agents on compositional tasks. Experiments demonstrate successful generation and refinement of five MRBTs, consistently improving training efficiency and task success rates over baselines and MRBTs without action masking. We further highlight three advantages of MRBTs: transferability, modularity, and verifiability.

While reinforcement learning (RL) promises to revolutionize the control of complex nonlinear robotic systems, a profound gap persists between the heuristic success of model-free off-policy deep RL and the underlying theory, which remains largely confined to tabular or linearizable settings. We identify the cause of this gap as an emergent isolation of three traditions: (i) measure-theoretic MDP foundations on general spaces limit their analysis to exact dynamic programming and ignore all error sources of a learning process; (ii) deterministic error propagation analysis addresses the approximation error via concentrability coefficients without a finite-sample analysis of the estimation error; and (iii) PAC generalization bounds characterize the estimation errors of simplified topologies. We bridge these traditions with a unified theoretical framework for fitted Q-iteration (FQI) on general measurable Borel spaces. Our main result provides a finite-sample, adaptive-data performance bound by chaining measure-theoretic probability with Bellman-operator contraction in Banach spaces. We prove that sequential Rademacher complexity controls Bellman-regression generalization under policy-dependent data collection. We further extend this analysis to provide the first cumulative, pathwise online regret guarantee for FQI in continuous spaces. These results lay the necessary foundations for the formal analysis of many modern deep RL algorithms.

We investigate the ability of transformers to perform in-context reinforcement learning (ICRL), where a model must infer and execute learning algorithms from trajectory data without parameter updates. We show that a linear self-attention transformer block can provably implement policy-improvement methods, including semi-gradient SARSA and actor-critic, via explicit parameter constructions. Beyond existence, we design a teacher-mimicking training procedure, analyze its gradient-flow dynamics, and establish the first convergence guarantee in the ICRL literature: under suitable richness conditions on the training MDP distribution, gradient flow converges locally and exponentially to an optimal parameter manifold corresponding to the desired RL update. Empirically, training transformers on randomly generated tabular MDPs confirms these predictions: the learned models recover the parameter structure of our explicit constructions and, when deployed on unseen MDPs, deliver strong in-context control performance. Together, these results illuminate how transformer architectures internalize and execute classical reinforcement learning algorithms in context, bridging mechanistic understanding and training dynamics in ICRL.

Transfer learning in reinforcement learning (RL) seeks to accelerate learning in new tasks by leveraging knowledge from related sources. Existing neurosymbolic transfer methods, however, typically rely on manually specified task automata, assume a single source task, and use fixed knowledge-integration mechanisms that cannot adapt to varying source relevance. We propose LANTERN, a unified framework for multi-source neurosymbolic transfer that addresses these limitations through three components: (i) deterministic finite automata generated from natural language task descriptions using large language models, (ii) semantic embedding-based aggregation of multiple source policies weighted by cross-task similarity, and (iii) adaptive teacher-student gating based on temporal-difference error and semantic uncertainty. Across domains spanning resource management, navigation, and control, LANTERN achieves 40-60% improvements in sample efficiency over existing baselines while remaining robust to poorly aligned sources. These results demonstrate that multi-source, adaptively weighted neurosymbolic transfer can improve scalability and robustness in symbolic RL settings.

A key capability of intelligent agents is to act effectively under incomplete state observations. Recurrent policies address this by compressing observation histories into a hidden state. In this work, we show that the hidden state of a recurrent policy admits a control-theoretic interpretation: it plays the role of the co-state in Pontryagin's minimum principle, and the readout that maps it to actions implements control-Hamiltonian minimization. The hidden state thus tracks the gradient of the value function, encoding the optimality structure of the underlying control problem. We formalize this correspondence through a class of policies we refer to as co-state policies (CPs) and show that several modern recurrent cells implicitly realize this structure. The correspondence also allows for a co-state loss for actor-critic training, in which the critic's gradient serves as a target for the actor's hidden state. Empirically, we find that hidden states trained with the co-state loss encode co-state information beyond what is linearly decodable from the environment state alone, and that the loss improves policies both within and outside this class on challenging locomotion tasks, including the H1 and Berkeley humanoids. By connecting the minimum principle to recurrent memory, we provide a control-theoretic account of what hidden states compute in continuous control and a mechanism for shaping them toward optimality.

Agentic reinforcement learning (RL) for software engineering spends much of its compute on stateful trajectories whose grouped binary rewards are highly skewed and weakly contrastive. We frame this as pass-rate control and show that the binary reward-side signal is strongest near a 50% rollout pass rate under four criteria: reward entropy, group-filtering survival, leave-one-out (RLOO) advantage energy under Group Relative Policy Optimization (GRPO), and success-failure pair count. We propose Prefix Sampling (PS), which replays self-generated trajectory prefixes to steer skewed groups toward this regime: successful prefixes give mostly failing groups a head start, while failing prefixes handicap mostly passing groups. Replayed states are reconstructed through the existing rollout path, and replayed tokens are masked from the loss so optimization applies only to current-policy continuations. On SWE-bench Verified, PS reaches the baseline high-score regime within evaluation variability while delivering 2.01x and 1.55x end-to-end wall-clock speedups on Qwen3-14B and Qwen3-32B; the 14B peak improves from 0.274 to 0.295. AIME 2025 experiments on 4B and 8B show the same pass-rate-control pattern, and 4B ablations attribute gains to replay, bidirectional coverage, and adaptive control.

Designing reward functions for agile robotic maneuvers in reinforcement learning remains difficult, and demonstration-based approaches often require reference motions that are unavailable for novel platforms or extreme stunts. We present LineRides, a line-guided learning framework that enables a custom bicycle robot to acquire diverse, commandable stunt behaviors from a user-provided spatial guideline and sparse key-orientations, without demonstrations or explicit timing. LineRides handles physically infeasible guidelines using a tracking margin that permits controlled deviation, resolves temporal ambiguity by measuring progress via traveled distance along the guideline, and disambiguates motion details through position- and sequence-based key-orientations. We evaluate LineRides on the Ultra Mobility Vehicle (UMV) and show that the policy trained with our methods supports seamless transitions between normal driving and stunt execution, enabling five distinct stunts on command: MiniHop, LargeHop, ThreePointTurn, Backflip, and DriftTurn.

Long-horizon LLM agents depend on intermediate information-gathering turns, yet training feedback is usually observed only at the final answer, because process-level rewards require high-quality human annotation. Existing turn-level shaping methods reward turns that increase the likelihood of a gold answer, but they require answer supervision or stable task-specific verifiers. Conversely, label-free RL methods extract self-signals from output distributions, but mainly at the answer or trajectory level and therefore cannot assign credit to intermediate turns. We propose Self-Induced Outcome Potential (SIOP), which treats semantic clusters of final answers as latent future outcome states for potential-based turn-level credit assignment. For each query, SIOP samples multiple rollouts, clusters final answers into semantic outcome modes, and builds a reliability-aware target distribution over these states. It then rewards turns for increasing posterior support for reliable future states using a tractable cluster-level approximation. The objective generalizes information-potential shaping from gold-answer supervision to settings without task-specific gold verifiers while avoiding the broadcasted rollout-level advantages used by standard GRPO. We formalize the framework, characterize its supervised gold-answer limit, and show that SIOP improves average performance over verifier-free outcome-level baselines on seven search-augmented agentic reasoning benchmarks while approaching a gold-supervised outcome baseline. Code is available at https://github.com/dl-m9/SIOP.git.

A cooperative robot swarm is a collective of computationally-limited robots that share a common goal. Each robot can only interact with a small subset of its peers, without knowing how this affects the collective utility. Recent advances in distributed multi-agent reinforcement learning have demonstrated that it is possible for robots to learn how to interact effectively with others, in a manner that is aligned with the common goal, despite each robot learning independently of others. However, this requires each robot to represent a potentially combinatorial number of interaction states, challenging the memory capabilities of the robots. This paper proposes an alternative approach for representing spatial interaction states for multi-robot reinforcement learning in swarms. A modular (decomposed) representation is used, where each feature of the state is handled by a separate learning procedure, and the results aggregated. We demonstrate the efficacy of the approach in numerous experiments with simulated robot swarms carrying out foraging.

Compositional generalization refers to correctly interpret novel combinations of known primitives, which remains a major challenge. Existing approaches often rely on supervised fine-tuning, which encourages models to imitate target outputs. This token-level training paradigm fails to capture the global compositional structure required for generalizing to unseen combinations. In this work, we investigate whether compositional generalization can instead be improved through outcome-level reinforcement learning. We adopt Group Relative Policy Optimization to optimize models based on feedback on their final outputs. Within this framework, we explore both a simple binary outcome reward and a composite reward that provides additional composition feedback. Experiments on multiple compositional benchmarks show that reinforcement learning improves compositional generalization compared to supervised fine-tuning. Further analysis reveals that supervised models tend to overfit frequent training compositions, whereas reinforcement learning improves compositional generalization by reshaping the output distribution, particularly for more complex composition types.

Recent research has revived and amplified interest in algorithms for undiscounted average reward reinforcement learning in infinite-horizon, non-episodic (continuing) tasks. Semi-Markov decision processes (SMDPs) are of particular interest. In SMDPs, discrete actions stochastically generate both rewards and durations, and the objective is to optimize the average reward rate. Existing algorithms approach this by optimizing the ratio of rewards to durations. However, when rewards and durations are non-stationary (in the infinite horizon), this can be incorrect. This paper presents a novel modified harmonic mean operator that correctly computes reward rates even under such conditions. This yields model-free learning algorithms that can work with SMDPs, while maintaining robustness to non-stationary reward and duration distributions over time. We prove theoretical properties of the modified harmonic mean operator, and empirically demonstrate its efficacy in comparison to existing algorithms.

In deep reinforcement learning (DRL), an agent is trained from a stream of experience. In a continual learning setting, such agents can suffer from plasticity loss: their ability to learn new skills from new experiences diminishes over training. Recently, Mixture-of-Experts (MoE) networks have been reported to enable scaling laws and facilitate the learning of diverse skills. However, in continual reinforcement learning settings, their performance can degenerate as learning proceeds, indicating a loss of plasticity. To address this, building on Neural Tangent Kernel (NTK) theory, we formalize the plasticity loss in MoE policies as a loss of spectral plasticity. We then derive a tractable proxy for spectral plasticity, one expressible in terms of individual expert feature matrices. Leveraging this proxy, we introduce SPHERE, a practical Parseval penalty tailored for MoE-based policies that alleviates the loss of spectral plasticity. On MetaWorld and HumanoidBench, SPHERE improves average success under continual RL by 133% and 50% over an unregularized MoE baseline, while maintaining higher spectral plasticity throughout training.

Recent analyses question whether reinforcement learning (RL) is responsible for strong reasoning in large language models (LLMs). At the same time, distillation and inference-time sampling, including power sampling, have emerged as effective ways to improve LLM performance. However, the relationship among RL, distillation, and sampling remains unclear. In this study, we focus on the power distribution, the target distribution of power sampling, and show that the power distribution bridges sampling, self-reward KL-regularized RL, and self-distillation. From the sampling perspective, we show that inexpensive local approximations cannot reproduce sequence-level power without information about possible suffixes. From the RL perspective, the power distribution is the closed-form optimizer of KL-regularized RL when the model's sequence-level log-probabilities are used as the reward. This identification leads to power self-distillation, an offline distillation surrogate that shares the same target distribution and amortizes the cost of power sampling into supervised training on teacher samples. We further show that power self-distillation can achieve self-reward sharpening, while improvement in a downstream true reward is governed by the covariance between true reward and self-reward under the power distribution. Experiments on reasoning tasks support our analysis: power sampling raises self-reward, true-reward gains depend on alignment with self-reward, and power self-distillation can match or exceed the performance of power sampling at much lower inference cost.

Open-loop imitation learning has advanced modern autonomous driving policy architectures, but closed-loop deployment remains vulnerable to policy-induced distribution shift. Existing post-training paradigms exhibit fundamental trade-offs: closed-loop RL fine-tuning provides grounded feedback from executed actions but is constrained by the sparsity of informative events, whereas counterfactual fine-tuning provides dense supervision over candidate futures but inherits bias from imperfect future estimates. We introduce Counterfactual-to-Interactive Reinforcement Fine-Tuning (CRAFT), an on-policy framework that formulates closed-loop post-training as proxy-residual optimization. CRAFT uses group-normalized counterfactual advantages as a dense proxy for real closed-loop advantages and aligns this proxy with the closed-loop world through grounded residual correction from interaction-critical events. To stabilize adaptation, CRAFT regularizes the online policy toward an EMA teacher via asymmetric KL self-distillation. Theoretically, CRAFT decomposes the real closed-loop policy gradient into proxy and residual terms under the same visited-state distribution, reducing residual variance with an aligned proxy while mitigating proxy bias through grounded residual approximation. Empirically, CRAFT achieves the strongest closed-loop gains on Bench2Drive across hierarchical planning, vision-language-action, and vocabulary-scoring architectures. Ablations, scaling behavior, stability analyses, and transfer results further validate the complementary roles of dense counterfactual proxy and grounded residual correction. Project page: https://currychen77.github.io/CRAFT.