Sparse-Reward RL

Recent agentic reinforcement learning methods use hindsight to complement sparse outcome rewards. However, a completed rollout can yield many such signals, leaving their appropriate allocation across turns unclear. We introduce TRIAL, a trajectory-relative hindsight distillation framework with a unified turn-aligned scoring protocol. For each decision turn, TRIAL extracts an outcome view of that decision's realized consequence and evaluates the same response under ordinary and hindsight-conditioned contexts. The signed log-probability gap determines the direction and local strength of token-level supervision, while turn-level magnitudes are normalized jointly over the realized trajectory. The resulting allocation multipliers have an eligible-token-weighted mean of one, redistributing dense supervision across turns while fixing its average multiplier. Experiments on WebShop and ALFWorld with different backbones show that TRIAL outperforms GRPO across all eight combinations of backbone, environment, and evaluation metric, while achieving the best or tied-best performance among six methods on six of them. On WebShop with Qwen3-1.7B, TRIAL improves the success rate from 56.4% to 75.2% and the task score from 78.7% to 85.7%. Controlled ablations further show that trajectory-relative turn allocation provides substantial gains beyond those of dense hindsight distillation alone.

Training large language model agents in long-horizon environments requires assigning credit from sparse terminal outcomes to individual actions. Existing critic-free methods propagate trajectory-level rewards uniformly across steps, while recent approaches construct step-level groups by matching repeated states and compare actions within each group. The former cannot distinguish useful actions in failed trajectories from ineffective actions in successful ones. The latter rely on step credit derived directly from individual trajectory outcomes and fixed-weight fusion with episode-level credit. We propose Gated-BEPO, which derives step-level credit from empirical rollout graphs. For each rollout group, Gated-BEPO constructs an empirical graph and estimates node values through a mean-backup Bellman fixed point that reflects the empirical action distribution of the current policy. We then accumulate these temporal-difference residuals along each sampled trajectory using generalized advantage estimation, yielding step-level Bellman advantages that capture both immediate and downstream effects. To adaptively fuse episode- and step-level credit, a confidence gate incorporates Bellman credit only at states with multiple observed successors and otherwise uses episode-level credit. Experiments on WebShop, ALFWorld, and visual Sokoban show consistent improvements across language and vision-language models, while diagnostic ablations support the effectiveness of Bellman fixed-point value estimation and show that step-level credit should be incorporated selectively rather than uniformly into the final advantage.

Agentic reinforcement learning enables LLM agents to learn through interaction, but sparse trajectory-level rewards reveal success without identifying which intermediate decisions deserve credit. Training-only privileged skills can provide denser supervision by allowing the same frozen policy snapshot to rescore fixed tokens from skill-free trajectories while conditioned on task-matched procedural skills. Existing methods, however, do not jointly calibrate teacher scores across interaction steps, relate teacher confidence to realized returns, and integrate the resulting signal into native reward-to-advantage construction. We introduce Agentic Reinforcement Learning with Self-Distilled Reward Shaping (ADRS), a framework for constructing return-associated token-level credit for multi-turn language agents. ADRS centers and normalizes privileged token scores within each step, modulates them with a return-associated Teacher Value Advantage (TVA) gate based on within-group confidence--return association, and incorporates the gated token signal into native RL credit construction. Together, these components determine what the teacher prefers, when that preference is return-relevant, and how it enters the native reinforcement-learning credit path, while keeping rollouts and inference skill-free. Finally, experiments across three interactive benchmarks show that ADRS consistently improves performance on long-horizon tasks, with gains persisting across RL backbones, reduced-data settings, unseen tasks, and extended training. For anonymous review, our code is available at the following the link: https://github.com/gitrxh/ADRS-arxiv

(Flat) Reinforcement Learning (RL) agents face significant challenges in environments with sparse rewards that require long-horizon reasoning. A compelling approach to improve sample efficiency is to incorporate knowledge into learning and decision-making. In standard Hierarchical RL (HRL), knowledge is encoded in a fixed, non-updatable form, such as architectural choices, and remains unchanged throughout learning. With fixed HRL, reasoning with incremental knowledge learned during exploration is impractical before sufficient environmental knowledge is acquired, leading to poor sample efficiency. In this work, we propose neurosymbolic HRL with {\em Incremental Knowledge (InK)}: symbolic high-level components perform {\em symbolic planning} (e.g. using $D^*$) on an updatable representation of current InK, while low-level goal-conditioned neural modules learn motion primitives through experience using reward shaping. Experiments on navigation tasks demonstrate that incorporating InK substantially improves sample efficiency. Additionally, to perform {\em optimal} symbolic planning given {\em prior} knowledge about the world, we develop Belief World Tree Search. The code is available at https://github.com/CPS-research-group/ink_bwts.

Large language model agents have shown strong potential in complex interactive tasks, yet their reinforcement learning (RL) is often hindered by sparse rewards, as a long multi-turn trajectory may receive only a single outcome-level signal. On-policy self-distillation (OPSD) provides dense token-level supervision from a privileged teacher, but the teacher may not be reliable at every position. Existing methods commonly rely on isolated token-level discrepancies, which can be sensitive to noise, or assign a shared step-level weight that may overlook positional variation. We propose Persistent Consistency Self-Distillation (PCSD), which derives token-level distillation weights from the local persistence of teacher-favoring signals. PCSD combines adaptive windows with exponentially decayed aggregation to capture persistent relative teacher support, applies trend-aware modulation to attenuate locally declining support, and produces continuous weights through sigmoid gating. The resulting objective is jointly optimized with GRPO, combining dense teacher guidance with sparse environmental feedback. Without inference-time skills, PCSD achieves the best ALFWorld Overall results among all baselines on both backbones, exceeding GRPO by 15.6 and 13.3 points and SDAR by 6.2 and 5.5 points, while remaining competitive on WebShop and gaining 15.8 points over GRPO on unseen ALFWorld split.

Multi-step search is a fundamental capability for search agents, enabling them to iteratively acquire, refine, and integrate external evidence for complex reasoning QA. However, vanilla GRPO allocates rewards exclusively based on the model's final outputs, yielding outcome-only supervision with no supervisory signals for intermediate reasoning steps. Such sparse supervision easily causes training instability and redundant search behaviors on multi-step search tasks. To mitigate this limitation, we adopt process reward to deliver stepwise supervision signals. For this process reward, we propose two complementary criteria to judge each search step: whether the step yields new evidence to facilitate problem solving, and whether it forms an efficient, pivotal intermediate decision within the overall reasoning trajectory. Building on this insight, we propose BiCAA: a bidirectional credit assignment framework that delivers dense, distinguishing process rewards for search-augmented agents. BiCAA builds bidirectional process rewards by fusing two complementary signals: forward solvability gain and hindsight success criticality. The former quantifies step-wise improvements in answer plausibility, while the latter evaluates each step's necessity for final success via hindsight outcome-based criticality scoring. We modulate and aggregate the two signals and then fuse them with the outcome reward. Experiments on search-augmented QA benchmarks show that BiCAA stabilizes policy optimization, reduces redundant search behavior, and achieves competitive performance.

In reinforcement learning, exploration with sparse and delayed rewards presents a significant challenge due to the limited feedback available for guiding the learning process. Addressing this issue requires extensive exploration in the state space to discover valuable reward signals. In this paper, we propose Entropic Information for Exploration (ENTINEX), a novel method that enhances exploration by incentivizing agents to explore beyond the boundaries of the state distribution. ENTINEX achieves this by assigning intrinsic rewards to these boundaries, leveraging entropic information to identify them effectively. Through extensive experimentation, we demonstrate that ENTINEX consistently improves exploration performance in environments characterized by sparse and delayed rewards. Our experimental results show that ENTINEX outperforms existing exploration methods, highlighting its effectiveness in both sparse and delayed reward scenarios.

Reinforcement learning has emerged as an effective paradigm for enhancing the mathematical reasoning capabilities of large language models. Among existing policy optimization methods, Proximal Policy Optimization (PPO) remains particularly appealing because its learned critic can, in principle, provide token-level credit assignment. However, in mathematical reasoning tasks characterized by long reasoning horizons and sparse outcome rewards, reliable token-level credit assignment remains challenging. The standard critic often fails to accurately evaluate intermediate reasoning states, resulting in noisy advantage estimates and suboptimal policy updates. In this paper, we propose ReDiPPO, a Reference-guided and Discrepancy-aware PPO framework for mathematical reasoning. ReDiPPO introduces a reference-guided critic that uses reference answers as training-time privileged signals to provide more accurate value estimation. Meanwhile, it retains a standard critic and quantifies the token-level reference-standard discrepancy between the standard value estimate and the reference-guided value estimate. This discrepancy serves as an indicator of difficult reasoning states and is used to reweight the corresponding token-level advantages during PPO optimization. Extensive experiments on diverse mathematical reasoning benchmarks demonstrate that ReDiPPO improves value-estimation accuracy and consistently outperforms strong policy optimization baselines, including PPO, DAPO, and GSPO, in final reasoning performance. Our code is available on https://github.com/cii030/ReDiPPO.

Sparse-reward reinforcement learning often fails because rollouts from the unassisted evaluation start rarely reach later task stages. Reset curricula address this by starting some training rollouts from easier intermediate states, called scaffolds. Such a curriculum faces two decisions: scaffold access, obtaining informative starts, and scaffold allocation, deciding how quickly that assistance is removed. Most prior curricula pace removal on one shared schedule, which can fail when task instances, or contexts, learn at different rates. We introduce SCOUT, an online, learner-agnostic reset controller that gives every context its own curriculum. Using only binary rollout success, SCOUT removes assistance after sustained success, restores it after failure, and cautiously tests a harder start when progress stalls, without changing the reward, optimizer, or learner. A counting construction shows that synchronized global pacing can be insufficient when contexts need conflicting amounts of assisted practice. Across six navigation and manipulation settings, scaffold access improves learning and enables success in three where unassisted training fails within the reported budget. In a constructed pacing conflict, each tested global schedule leaves one group unsolved, while SCOUT solves both. Average success can conceal this failure, so we also report the least successful group. Group-level pacing works when learning differences follow known groups but can fail when they occur within one group. SCOUT needs no group labels and remains consistently strong in both cases. A reset curriculum should remove assistance at the scale where learning progress differs.

Exploration in sparse-reward long-horizon tasks poses significant challenges for reinforcement learning. To address these challenges, we propose a two-level Hierarchical Reinforcement Learning (HRL) framework. The first level handles high-level strategic planning, while the low-level uses the continuous-control Soft Actor-Critic (SAC) algorithm, and they utilize entropy-regularized policy optimization. The proposed framework was trained and evaluated using the Search-and-Rescue-2 (SAR-2) dataset. HRL-SAC effectively addresses sparse-reward long-horizon search problems characterized by delayed rewards and continuous control, and its outperforming the flat SAC baseline reinforcement learning in terms of success rates, coverage efficiency, and convergence. These findings indicate that hierarchical entropy-regularized policies are a promising solution to tackle long-horizon sparse-reward reinforcement learning tasks.

Long-horizon manipulation tasks pose significant challenges for reinforcement learning due to sparse reward signals and long horizons. Automatic curriculum learning (ACL) has been proposed to tackle these challenges by progressively training agents on a sequence of tasks, from easier to more difficult. However, the success of ACL depends heavily on task-dependent specifications-such as well-defined task parameter spaces and difficulty measures-which are often manually crafted and difficult to generalize across diverse tasks. Recent advances in large language models (LLMs) offer a promising alternative by enabling the decomposition of complex tasks into meaningful subtasks using the LLMs' web-scale common-sense knowledge. This decomposition can provide a natural curriculum structure for efficient learning of long-horizon tasks. However, existing LLM-based methods typically rely on hand-designed dense reward functions to learn each subtask, which can introduce bias and still requires significant human supervision. In this work, we propose LLM-enhanced automatic curriculum learning (LEACL), a framework that integrates LLMs and ACL to address these limitations. Specifically, LLMs are used to both decompose tasks into subtasks and to generate task-dependent specifications for each subtask. These specifications are then used by ACL algorithms to guide learning using only sparse reward signals, eliminating the need for dense reward design. We evaluate LEACL on five long-horizon manipulation tasks from the LIBERO benchmark. LEACL achieves better asymptotic performance in terms of the success rates compared to human-designed dense rewards.

Dense per-step supervision is the standard remedy for sparse-reward long-horizon LLM agents: reward the policy for predicting its next observation, which looks provably safe under potential-based shaping. Published prediction-reward and auxiliary-loss variants report both successes and instabilities; we supply the controlled account: 74 preregistered arms dissect one fixed prediction signal under GRPO across ALFWorld, WebShop, a synthetic POMDP, and Qwen3-1.7B/4B/8B, varying only the delivery mechanism. (1) Every run sustaining this difference-form reward under untouched std normalization (no filtering, dynamic-sampling, or decoupling mitigations) collapses: eleven runs across scales, coefficients, group sizes, and groupings (the floor-bound synthetic environment stalls instead); ALFWorld runs end in an absorbing state (prediction accuracy -> 1.0, success -> 0): the optimizer builds the "dark room". The algebra is one line: in all-fail groups z-scoring cancels the shaping coefficient; removing only std normalization restores baseline parity. (2) A signal's danger is set by its within-group variance trajectory, plus hackability as a second axis; it retrodicts every reward-channel collapse and survives preregistered prospective tests. (3) The same signal as a teacher-forced auxiliary loss is harmless on ALFWorld at 4B, but the gain is not the signal's: content-free placebos as a class match or beat gold at both matched seeds (s0: 78.8 vs 68.6; s42: 67.9 vs 57.9); the auxiliary update is the regularizer. (4) At 8B the recipe turns bistable: gold full-weight locks two of three seeds; every content-free or reduced-weight arm stays healthy. No ALFWorld or WebShop reward-channel variant measurably beats its matched-normalization baseline and no gold signal measurably outperforms its content-free placebo: the delivery channel, not the content, decides; which channel is safe is regime-dependent.

Group-based policy optimization has been increasingly used to train large language model (LLM) agents from sparse outcome rewards by comparing trajectories or steps within a group. However, on difficult long-horizon tasks, this comparison can suffer from a sampling imbalance: repeated or low-effect actions dominate the high-probability region of the policy while useful state-changing actions remain under-sampled. This imbalance produces many all-failed rollout groups, where outcome rewards provide no direction for correcting the policy. Together, these effects can form a self-reinforcing credit trap: failure-dominated sampling yields no outcome-based correction, allowing repeated low-effect actions to persist. To break this loop, we propose Progress-conditioned Group Policy Optimization (ProGPO), which uses first-visit observation coverage only when all samples in a group receive zero outcome reward. Specifically, within such groups, ProGPO assigns higher relative advantages to trajectories or steps that visit more new states since reaching new observations is a prerequisite for task success. Experiments on two challenging agentic benchmarks, ALFWorld and WebShop with Qwen2.5-1.5/7B-Instruct, show that ProGPO consistently improves over group-based baselines, with particularly large gains on hard tasks.

Hierarchical Reinforcement Learning (HRL) intends to separate strategic planning from primitive execution. It has been widely successful in solving long-horizon and complex tasks, where flat-RL algorithms have difficulty in learning. However, while the low-level agent in HRL benefits from dense feedback and abundant trial opportunities, the high-level agent receives sparse, delayed feedback from the environment and its performance depends on the low-level execution capability. In this paper, we study whether subgoal selection by the high-level agent can be performed more strategically, by providing it with dynamics-aware intrinsic motivation. Since motivation based on primitive transition dynamics would require broad coverage of the state-action space, we propose to use coarse dynamics, i.e., environment transitions aggregated over multiple steps at the temporal scale at which the high-level agent operates. This approach stabilizes the high-level policy by learning to minimize the predictive uncertainty associated with the coarse dynamics, and provides a guided structure for navigation. We model the predictive uncertainty by evaluating different dispersion metrics as approximated by a Mixture Density Network (MDN). Empirically, we observe that a dense, dynamics-aware intrinsic reward leads to risk-averse subgoal selection, enabling it to outperform state-of-the-art HRL methods in non-stationary long-horizon environments.

The Credit Assignment Problem (CAP) is fundamental to developing efficient and explainable Reinforcement Learning (RL) agents. Existing frameworks, whether relying on temporal contiguity or hindsight-conditioned reward reweighting, frequently fail to attribute properly between an agent's policy (skill) and environmental stochasticity (luck). A principled approach to CAP must isolate the true causal drivers of observed outcomes from spurious correlations and environmental randomness. We introduce Counterfactual Shapley Credit Assignment, a novel framework grounded in causal theory that attributes credit and blame via the Counterfactual Shapley Value ($φ$-value). By redistributing environmental rewards, $φ$-values enhance temporal credit assignment across three critical dimensions: sparse causality, high stochasticity, and delayed rewards, all while preserving the optimal policy. We derive a consistent estimator that computes $φ$-values efficiently, enabling a new class of policy gradient methods, $φ$-PPO, combined with Prioritized Trajectory Replay (PTR). Empirical results demonstrate that $φ$-values align precisely to the ground truth causes of task rewards with superior sample efficiency in challenging environments where prior state-of-the-art methods fail to converge.

Temporal Knowledge Graph (TKG) reasoning under the extrapolation setting focuses on forecasting future time-stamped events (facts) from historical data in a temporal knowledge graph. Existing approaches, reinforcement learning (RL)-based multi-hop reasoning methods are prominent for TKG reasoning because they produce human-interpretable predictions via explicit multi-hop path tracing. However, during RL training, rewards are typically sparse, and exploration is highly inefficient due to the vast, time-evolving action space. These issues hinder efficient training and often limit overall performance. To address these challenges, we propose RAPTOR (Reachability-Aware Pretraining for Efficient Target-Oriented Path Exploration), a self-supervised pretraining method that injects a reachability-aware inductive bias to the agent. By learning to estimate the reachability of candidate actions to the target entity, RAPTOR reduces exploration over unpromising paths and provides a strong initialization for downstream RL fine-tuning. Experimental results on the ICEWS14, ICEWS05-15, and ICEWS18 datasets demonstrate that RAPTOR pretraining markedly improves the training efficiency and consistently outperforms conventional baselines, establishing it as an effective approach for enhancing RL-based multi-hop reasoning methods for TKG reasoning.

Large language models are increasingly trained as interactive agents for long-horizon tasks involving multi-turn interaction, tool use, and environment feedback. Outcome-based reinforcement learning (RL) provides a practical optimization paradigm, but its sparse trajectory-level rewards offer limited guidance on intermediate decisions, leaving a supervision gap between episode-level outcomes and token-level policy learning. We propose SEED (SElf-Evolving On-Policy Distillation), a self-evolving framework that converts completed on-policy trajectories into training-time hindsight skills and distills their behavioral effect back into the policy model. SEED first fine-tunes the policy to analyze completed trajectories and generate natural-language skills that capture reusable workflows, decisive observations, or failure-avoidance rules. During RL, the current policy both collects trajectories and serves as the analyzer that extracts hindsight skills from them. Policy updates therefore improve subsequent decision making and skill analysis together, allowing hindsight supervision to evolve with the policy. SEED then re-scores the sampled actions under ordinary and skill-augmented contexts, converting the skill-induced probability shift into a dense token-level on-policy distillation signal. This signal is jointly optimized with outcome-based RL, keeping the auxiliary supervision aligned with the current trajectory distribution. Extensive experiments on text-based and vision-based agentic tasks show that SEED consistently improves performance and sample efficiency, exhibiting robust generalization to unseen scenarios. Our code is available at https://github.com/jinyangwu/SEED.

AlphaZero has demonstrated that a neural-guided Monte Carlo Tree Search can achieve superhuman performance, but strong play does not necessarily imply perfect play. We study this gap in two oracle-evaluable domains with contrasting structure: Connect Four, a solved partisan game with exact game-theoretic values, and Chomp, an impartial game whose optimal play is governed by Grundy-number structure. Under a unified self-play $+$ MCTS pipeline, we compare vanilla AlphaZero, a multi-frame variant (limited to Chomp), and an AlphaZero Auxiliary Loss (AZAL) that adds oracle-derived policy supervision. We find that vanilla AlphaZero achieves strong play across both domains but cannot preserve the exact trajectories required for optimal play: in Connect Four, it fails to maintain the optimal line of play, while in Chomp, it fails to consistently restore the $g=0$ invariant. On rectangular Chomp boards, multi-frame inputs alone do not remove this gap. Nevertheless, AZAL substantially improves oracle consistency across multi-seeded full-game traces and sampled-state evaluations. On Chomp, AZAL reaches perfect full-game oracle consistency on 10x11 and high but not complete consistency on 9x10; on Connect Four, AZAL improves oracle-match rate and delays the first oracle mistake, but does not reach perfect play.

Reinforcement Learning (RL) is the dominant paradigm for training Large Language Model (LLM) agents on long-horizon tasks. However, sparse and delayed rewards often lead to trajectory neglect, in which agents lose focus on the task goal and interaction history at intermediate steps. Prior work has explored step-level supervision using Shannon-entropy-based uncertainty signals, which conflate inherent state complexity with agent confidence and therefore provide unreliable estimates of decision reliability. To address this issue, we propose normalized entropy, which measures confidence deviations relative to an agent's average behavior under a given state, thereby strengthening the association between low-quality actions and trajectory neglect. Building on this insight, we introduce Selective Trajectory-Aware Policy Optimization (STAPO), a hierarchical group-based RL framework. STAPO leverages normalized entropy to locate outlier steps associated with trajectory neglect and optimizes them via a joint mechanism of trajectory-aware reward and trajectory-independent penalty, enhancing trajectory awareness while preserving training stability. Extensive experiments on ALFWorld, WebShop, and Search-Augmented QA demonstrate that STAPO achieves state-of-the-art performance while substantially alleviating trajectory neglect, validating its effectiveness and robustness for agentic tasks.

Reinforcement learning holds significant potential for training large language models (LLMs) to handle multi-turn interactive tasks. However, in long-horizon, multi-turn tasks characterized by sparse outcome rewards, directly training with outcome rewards often results in slow convergence due to the sparsity of signals and the lack of fine-grained feedback. Furthermore, the model may fail to learn successful trajectories that are not sampled during training, thereby limiting its performance. Conversely, while employing customized dense process rewards provides richer signals and accelerates convergence, these surrogate rewards may exhibit potential misalignment with the ground-truth outcome rewards. This inconsistency can bias the training direction and ultimately degrade the model's final performance. In this work, we propose Reward-Swap Policy Optimization (RSPO), a method designed to leverage the rich information from dense process rewards to facilitate training with outcome rewards. By utilizing a reward-swap mechanism, RSPO ensures the diversity of sampled trajectories while guaranteeing consistency between the optimization objective and the true outcome rewards, thereby elevating the performance ceiling of the model. We conduct extensive experiments on two challenging agent benchmarks, WebShop and ALFWorld. By applying our method to various reinforcement learning algorithms, including GRPO, PPO, and GiGPO, we demonstrate that RSPO achieves consistent performance improvements across different baselines and benchmarks.

Reinforcement Learning (RL) has substantially improved the reasoning ability of large language models (LLMs), but sparse outcome rewards still make token-level credit assignment difficult. Existing scalable RL methods typically assign trajectory-level rewards uniformly across tokens, while recent entropy-aware approaches either rely on coarse detached heuristics or directly optimize true entropy, which can introduce non-local gradient components misaligned with sampled-token policy updates. We propose Adaptive Credit Policy Optimization (ACPO), a token-level credit assignment framework based on a mode-local surrogate entropy. ACPO asymmetrically modulates policy updates by emphasizing uncertain decisions in successful rollouts and overconfident tokens in failed rollouts. We show that the surrogate admits deterministic entropy bounds and, under modal alignment and proximal updates, preserves the policy-gradient direction to leading order. Experiments on mathematical reasoning and coding benchmarks, including AIME 2025 and HumanEvalPro, show that ACPO consistently improves over strong RL baselines such as DAPO, GTPO, and SAPO.

Real-time strategy (RTS) games present significant AI challenges, characterized by expansive state-action spaces arising from multi-unit coordination in continuous battlefields, and sparse delayed rewards stemming from final win/lose signals. Existing approaches face a trade-off between managing the dimensionality explosion of joint actions and maintaining the interpretability of complex state representations. This complexity is further intensified by the limitation of traditional hierarchical structures in adaptively decomposing tasks into effective tactical modules. Such difficulties are compounded by the black-box nature of deep learning models and their reliance on sparse rewards, which together result in limited sample efficiency and a lack of decision-making transparency. To address these limitations, this paper proposes HRL-IM/CBS, a hierarchical reinforcement learning framework with influence map hashing and cluster-based scripts for StarCraft micromanagement. Influence map hashing encodes global battlefield situations into compact hexadecimal codes, capturing spatial control and relative advantage. Cluster-based scripts enable dynamic local coordination through adaptive unit partitioning. The hierarchical multi-Q-table architecture decomposes decision-making into upper-level clustering strategy selection and lower-level tactical execution, with reward allocation providing dense learning signals. Experiments across six asymmetric scenarios demonstrate competitive performance against deep RL baselines while offering advantages in sample efficiency and interpretability through transparent Q-table representations.

Agentic search equips large language models with dynamic retrieval abilities, but existing reinforcement learning methods remain limited by reward sparsity in knowledge boundary calibration -- deciding when to trust parametric memory, when to rely on retrieved evidence, and when to abstain. Binary rewards can penalize undesirable outcomes, but provide little guidance on the reasoning process required to make calibrated decisions across different knowledge states. To address this, we propose KbSD (Knowledge boundary Self-Distillation), a framework that tackles this limitation through dense token-level supervision, outcome-level sparse rewards, and quadrant-adaptive optimization. KbSD constructs a hint-augmented teacher, architecturally identical to the student, that receives explicit knowledge boundary signals -- including parametric certainty, retrieval quality, and ground-truth answers -- to generate calibrated reasoning demonstrations. This information-asymmetric self-distillation enables dense supervision without requiring a larger external model. To further account for the heterogeneous reasoning distributions across knowledge states, we introduce a quadrant-adaptive distillation objective: reverse KL for concentrated integration, forward KL for diverse refusal, and Pareto-optimal bidirectional KL for asymmetric quadrants requiring both precision and coverage. Experiments on multiple benchmarks show that KbSD consistently improves both task accuracy and hallucination mitigation over strong baselines, with the largest gains appearing in the challenging quadrants where sparse rewards are least informative.

Sparse rewards are inherently challenging for reinforcement learning agents as they lack intermediate feedback to guide exploration and to correctly attribute the sparse success rewards to relevant parts of the trajectory. Naive reward shaping can induce reward hacking, yielding policies that exploit auxiliary signals instead of solving the intended task. Potential-based reward shaping (PBRS) guarantees preservation of the optimal policy set, but requires the definition of a heuristic potential function over the state space. In this work, we introduce the VLM-guided PBRS framework VLM-PBRS that learns the potential function directly from vision language model (VLM) feedback. We query a lightweight VLM to obtain preferences over image pairs and train a model of the potential function using these preferences. As this approach is based on potential-based reward shaping, it preserves the original optimal policies, and removes the need for expert-designed reward shaping terms. Because large VLMs are prohibitively expensive to invoke repeatedly during policy learning, we employ smaller, more computationally efficient VLMs. Although the resulting preference labels are less accurate, empirical evidence shows that the preference labels can still be used to accelerate learning. We validate our method empirically in the Meta-World and Franka Kitchen environments and highlight the connection between VLM preference label accuracy and sample efficiency improvements. Our contributions are threefold: (1) the first application of VLM preference-based learning to synthesize a potential function for PBRS, (2) a principled, low-cost solution that leverages small VLMs, and (3) extensive empirical demonstration of improved sample efficiency and robustness to reward hacking.

Reinforcement learning in large or sparse-reward environments suffers from slow temporal-difference reward propagation, as value information spreads only locally across the state space. We propose Mesh-RL, a spatial domain-decomposition framework inspired by the finite element method and domain decomposition theory, which partitions the environment into overlapping subgrids and enforces boundary-consistent temporal-difference updates. Such an approach enables localized learning while ensuring globally coherent value propagation. Unlike hierarchical or model-based approaches, Mesh-RL accelerates long-range credit assignment without modifying the reward function, Bellman operator, or introducing explicit planning mechanisms. We evaluate Mesh-RL on hazard-dense grid-world environments with varying geometries and mesh resolutions. Across Q-learning, SARSA, and Dyna-Q, Mesh-RL consistently improves convergence speed, cumulative reward, and learning stability. Higher mesh resolutions sustain exploration, prevent premature convergence, and substantially accelerate value propagation to distant states. While Dyna-Q already benefits from internal planning, it still achieves additional gains under structured decomposition. Overall, Mesh-RL introduces a principled spatial domain-decomposition mechanism for accelerating temporal-difference learning. Our framework bridges finite element method-inspired boundary-consistency techniques from scientific computing with reinforcement learning to improve sample efficiency in sparse-reward environments. We will release source code of the study.

Group-based reinforcement learning effectively post-trains LLM agents for long-horizon, sparse-reward tasks by deriving step-level credit from trajectory outcomes. However, this ties a step's credit to its rollout's final outcome: semantically near-identical intermediate steps receive opposite credit depending on whether their trajectory eventually succeeded or failed. Such semantic credit inconsistency sends conflicting gradients to similar actions and wastes the partially-correct progress inside failed rollouts. Motivated by this, we propose Semantic Consistency Policy Optimization (SCPO), a value-free reward-shaping method that mitigates this inconsistency by recovering step-level credit from successful siblings in the same rollout group. Concretely, SCPO scores each failed step against a successful sibling and adds positive step-level credit for new progress along that sibling. On ALFWorld and WebShop, SCPO matches or exceeds strong group-based baselines, reaching 93.7+/-4.1 percent success on ALFWorld and 74.8+/-2.0 percent on WebShop at 1.5B parameters, with gains concentrated on the hardest multi-step tasks.

Estimating token-level advantages in reinforcement learning (RL) for language models remains challenging because scaling up episodic experience collection is expensive. The difficulty intensifies for baseline advantage estimation methods, where repeated sampling causes trajectories to diverge into substantially different reasoning prefixes. In this context, RL algorithms such as GRPO prove limited: an outcome reward is too sparse to be attributed to specific actions like intermediate steps, and comparisons across sampled traces are non-trivial because they are heterogeneous. To mitigate both the computational cost of repeated sampling and the difficulty of credit assignment, we study single-rollout proximal policy optimization (SR-PPO) featuring token-level credit assignment in RL for language models. Instead of estimating advantages by normalizing episodic returns within the candidate group, we train a calibrated token-level credit critic using Monte Carlo outcomes from one rollout per prompt. Specifically, we use the critic to predict the Pass@k success probability at the prompt prefix, which is derived from a Pass@1 attempt. This choice yields a more selective learning signal than Pass@1: it discounts easily solved prefixes while prioritizing hard ones whose success probability remains marginal. We show that as $k$ increases, Pass@k converges to a reachability indicator, reflecting whether a prefix can lead to at least one successful continuation. In an explicit state graph, the limit ($k \rightarrow \infty$) can be computed in $O(|V|+|E|)$ time, offering a promising surrogate for direct credit assignment without the need to sample contrastive traces. As an initial validation, SR-PPO exhibits stable learning dynamics, along with consistent gains in Pass@128 success rates on mathematical reasoning benchmarks such as HMMT26 and AIME24.

In many modern applications of reinforcement learning (RL), the natural reward for a task of interest is inherently sparse: a reward of 0 is given everywhere except when the task is completed, when a reward of +1 is given. Training a policy to maximize such a sparse reward requires solving a challenging credit assignment problem, leading to slow or ineffective RL improvement. We propose a simple approach to transform a sparse outcome reward into a dense process reward. Our approach relies on training a discriminator to distinguish between previous successful and unsuccessful episodes, and using this discriminator to incentivize the RL-learned policy to match the state-action visitations of successful episodes, while avoiding those of unsuccessful episodes. By incentivizing the policy to match the visitations over all states, not just those that correspond to task success, this reward provides dense feedback on whether progress is being made towards task completion, and, we show, provably achieves this without changing the optimal policy. Focusing on finetuning of robotic control policies, we demonstrate that our approach leads to significantly faster RL finetuning performance on both simulated and real-world manipulation tasks, as compared to simply maximizing the sparse outcome reward.

Group-based Reinforcement Learning (RL) has significantly enhanced Large Language Models (LLMs) in agentic scenarios. To achieve finer-grained policy updates, recent agentic RL frameworks have shifted from trajectory-level to step-level training. However, long-horizon agentic RL suffers from severe reward sparsity and delay, as feedback is often deferred for dozens of interaction steps. While existing step-level frameworks refine training granularity, their credit assignment remains coarse-grained and still treats agent exploration as isolated, linear trajectories. This oversimplified perspective ignores the inherent graph structure of state transitions, leading to high-variance state-value estimation and myopic, localized credit assignment. To overcome these critical bottlenecks, we propose Group-Graph Policy Optimization (G2PO), a novel group-based RL algorithm tailored for multi-turn agentic tasks. G2PO explicitly transforms linear interaction trajectories into a global state-transition graph. By aggregating identical observations across different trajectories, we introduce group-aggregation state-value estimation that reduces sampling variance and trajectory-dependent bias. Furthermore, we redefine agent actions as transitions between state nodes and propose an edge-centric advantage estimation strategy. By globally standardizing Temporal Difference (TD) errors across the entire graph, G2PO explicitly identifies and prioritizes critical transitions that drive absolute task progress. Extensive experiments on representative long-horizon benchmarks-WebShop, ALFWorld, and AppWorld-demonstrate that G2PO substantially outperforms state-of-the-art prompt-based and RL baselines, achieving remarkable success rate improvements of up to 22.2% over GRPO.

Applying machine learning techniques to solving long-standing mathematical conjectures can be particularly challenging due to their extreme reward sparsity. As an illustrative example, we consider Kalai's algebraic Hirsch conjecture and recast the construction of its counterexamples as a sparse-reward reinforcement learning problem on graphs. We propose a constrained options-based HRL framework with an equivariant graph neural network policy, which allows us to learn useful temporal abstractions for this task. We evaluate our approach over a wide range of degrees and demonstrate that it consistently outperforms classical RL algorithms as well as greedy search. By exploiting the hierarchical structure of the problem, we effectively provide a first-of-its-kind application of HRL to a problem in commutative algebra.