Credit Assignment

When an agent handling a payment exception loses money, the agent-step attribution methods this paper compares against will name one of its actions. They will do so even when a settlement message was dropped and the agent never had a chance: they intervene on agent actions and do not expose infrastructure faults as intervenable variables, so every dollar they explain is charged to a decision. We take a benchmark whose fault process is explicit and replayable, decompose each episode's realised delivery schedule into named, individually repairable messages, and intervene on both the agent's choices and the infrastructure's. A telescoping identity splits any policy's loss exactly three ways: an infrastructure effect, a policy differential against the best implementable policy, and a reference-policy residual. Two of the three can be negative, so none is a share; Shapley then divides the first into signed allocations over individual messages. One result is structural and needs no corpus: an agent-only baseline identifies no infrastructure cause, because its model contains no variable that could name one. What 545 planted episodes across 3 policies measure is the size of that consequence. It misfiles 100% of infrastructure episodes and charges $114,383.40 to the agent. Repairing what it names recovers 0.0% of the available loss; repairing a minimal sufficient set recovers 100.0%. Scoring messages one at a time is not merely imprecise: 27.8% (95% CI: 23.3--32.3%) of episodes do not decompose additively. We evaluate deterministic programmatic policies rather than language-model agents, which is what makes replay exact and which limits external validity to stochastic agents. The prevalence figures are properties of this generator, not field rates.

Reward-based reinforcement learning for language models, exemplified by Group Relative Policy Optimization (GRPO), collapses an entire stochastic trajectory into a single scalar reward. This is clean and scalable, but it explores and allocates reward inefficiently: a trajectory may contain many causal decisions, recovery attempts, and environment-randomness events, yet every token or action inherits one trajectory-level advantage. We study tree-based rollout construction as a compute-allocation problem for policy-gradient estimation. Our central claim is that branches should be placed not where the policy is merely uncertain, but where an additional branch most reduces uncertainty about the policy gradient per unit of compute. From a law-of-total-variance decomposition of the local policy-gradient random variable, we derive two allocation laws: new branches reduce decision uncertainty, while repeated suffix rollouts reduce continuation uncertainty. The resulting EPIG-Tree score allocates branches using the already computed rollouts. It estimates occupancy- and score-weighted value uncertainty, along with a suffix law $n_e \propto w_e \|\nabla_θ\log π(a_e|h_e)\| σ_e / \sqrt{c_e}$. Empirically, EPIG reduces gradient MSE in cloned-state control, winning in all nine dense continuous-control environments of a 13-environment sweep and recovering the reference gradient direction near-perfectly, and it improves frozen-LLM gradient calibration relative to entropy branching. In online single-turn math, tree-local credit beats flat GRPO, while branch placement is secondary to token-level credit assignment. In online multi-turn Wordle, EPIG attains the highest final win rate (0.850), overtaking flat GRPO, which saturates early at 0.790, and entropy branching as training proceeds, confirming that the gradient-estimation advantage transfers to a stateful, large-action setting.

Generative query suggestion aims to enhance user engagement by anticipating user intents and recommending relevant follow-up queries. A central challenge is to generate slates whose individual queries are useful while the slate covers distinct intents. We propose an Intent-Driven Query Suggestion Framework with dual-stage optimization. First, intent-aware diversity modeling constructs intent-aligned supervised fine-tuning (SFT) data and uses an Intent-Aware Diversity Reward to optimize intent coverage. Second, query-level credit assignment routes individual quality signals to the corresponding query tokens while sharing a slate-level diversity signal across the slate. Experiments on a large-scale production dataset, including online A/B testing and offline evaluation, show improvements in click-through rate, query quality, and intent coverage.

On-policy distillation (OPD) has emerged as an effective approach for large language model post-training, yet existing objectives face a trade-off between objective fidelity and optimization stability. Token-level OPD provides stable but local supervision, whereas sequence-level OPD captures future credit at the cost of horizon-dependent variance. We establish a unified temporal-credit view of these formulations, showing that practical token-level OPD can be interpreted as a temporal approximation to the sequence-level reverse-KL gradient. Building on this connection, we propose $γ$OPD, which uses discounted temporal credit assignment to balance long-horizon supervision and optimization stability, while admitting a horizon-independent variance bound. We further develop a reward-compatible bounded mixing (RBM) mechanism for $γ\mathrm{OPD}$ that balances verifiable outcome feedback with the discounted OPD advantage to move beyond purely teacher-dependent optimization. Experiments on mathematical and code reasoning demonstrate consistent improvements over existing OPD methods across vanilla, size-mismatched, and multi-teacher distillation settings.

Reinforcement learning with verifiable rewards (RLVR) has become a central approach for improving mathematical reasoning in language models, but long-form completions introduce a difficult credit-assignment problem: different parts of a solution trace may contribute unevenly to final correctness. Existing policyoptimization objectives for RLVR commonly apply importance-sampling correction at either the token level (GRPO, DAPO) or the sequence level (GSPO), imposing different granularities for assigning credit across a response. We introduce Hierarchical Importance-Sampling Policy Optimization (HISPO), a segment-level policy-optimization method that constructs rollout-time entropy-derived contiguous segments, assigns soft entropy-based saliency weights, and applies clipped importance-sampling correction at the segment granularity. This provides an intermediate correction unit between token-level GRPO/DAPO and sequence-level GSPO. We evaluate HISPO by fine-tuning Qwen3-1.7B-Base on mathematical reasoning tasks. Across six benchmarks, HISPO improves Pass@8 over the strongest baseline on all benchmarks and matches or exceeds the strongest baseline in Acc@8 on five of them. On AIME25, HISPO improves over GRPO by +3.75 Acc@8 and +3.78 Pass@8, and over GSPO by +2.50 Acc@8 and +1.27 Pass@8. These results suggest that segment-level correction is a promising granularity for RLVR in long-form mathematical reasoning.

Reinforcement learning is now the standard way to train large language model agents on long-horizon tasks, where dozens of interdependent actions precede a single sparse reward. Critic-free, group-relative methods such as GRPO suit this regime, but they broadcast one trajectory-level scalar to every step and cannot say which decision drove the outcome. GiGPO recovers a step-level signal by grouping time steps that share an anchor state, yet it merges the step- and episode-level estimates under one fixed weight, spending the same resolution on a pivotal branching decision as on a routine, near-deterministic transition. We argue that the right resolution is state-dependent, and propose GACA, a critic-free estimator whose granularity follows an uncertainty-based criticality proxy. GACA scores every step by the negative log-likelihood its own rollout already records, then blends the two advantages with a per-step weight that grows with that score, so the gradient places more weight on the fine-grained signal at above-average NLL and on the episode-level signal below it. We derive an exact risk decomposition for the implemented mixture and show that sufficiently small modulation improves on fixed mixing under positive directional alignment. A separate conditional result bounds local action-value variation using expected NLL, while an error-projection analysis characterizes when mixing adds value beyond scalar uncertainty reweighting. On ALFWorld and WebShop, GACA improves task success over GRPO and GiGPO at both 1.5B and 7B scales.

In autoregressive forecasting, long prediction rollouts provide distant supervision, but backpropagation through time (BPTT) carries gradients from those losses through many autoregressive steps. Repeated Jacobian products can make distant gradients dominate the update while amplifying predictable signal and unpredictable noise together; a large distant gradient therefore need not carry reliable learning signal. Motivated by this observation, we introduce Internal Dual-Wiener routing (Internal-DW), a principled backward-only intervention that preserves the full forward rollout and all horizon losses while reliability-weighting internal gradient routes. At each residual block, we derive bounded Wiener gains for the identity and nonlinear routes that balance preserving predictable learning signal against suppressing unpredictable variation, and estimate them from route-level gradient statistics and an explicit noise model. In a controlled system with known gradient signal-to-noise ratio (SNR), we show that distant gradients can grow even as their SNR falls, and that Internal-DW reduces held-out error in recovering predictable gradient signals and improves forecasting. On four history-dominated, weak-drive testbeds, Internal-DW reduces forecast error by 5.2%-13.8% relative to full BPTT, outperforms gradient clipping and Jacobian regularization on all four, and outperforms validation-selected truncated BPTT (TBPTT) on three. It also extends or preserves the fitted optimal training-horizon range across these four testbeds. Across the full benchmark suite, the current Internal-DW estimator has a clear applicability boundary: its benefit diminishes or reverses when usable history is limited or when the selected sampler fails to represent dominant drive-dependent variation. The results show that retaining long-horizon supervision does not require trusting every backward contribution equally.

Agent reinforcement learning (RL) increasingly runs through full execution harnesses, and a multi-harness recipe mixes two choices: exposing the policy to several harnesses, and comparing their rewards inside one relative-advantage group. We isolate the second choice in repository-level coding. From one Qwen3-8B supervised warm start we replay the same frozen task-harness records from Aider, OpenHands, Qwen Code, and SWE-agent, with the same number of updates, under two rules for group-relative policy optimization (GRPO), Within (one group per task-harness pair) and Cross (harnesses pooled within a task), and score every checkpoint with a sealed SWE-bench Verified oracle on four source harnesses and a minimal harness held out of training. The evaluation harness is the dominant variable: across 24,000 sealed evaluations it moves the mean solve rate from 2.14% to 9.27%, a factor of 4.3, where the training recipe moves it by 1.16. The grouping rule is not. On the held-out harness, Cross minus Within is +0.25 pp, 95% confidence interval [-0.48, +1.02], at eight attempts per task, and +0.16 [-0.41, +0.72] pooled over three training seeds whose individual estimates change sign. Each rule's own seed range, 0.42 to 0.45 pp, exceeds the difference between them. Both rules place their largest gains on the same source harness. The pooled advantage carries the harness: an out-of-fold classifier recovers the generating harness from Cross's advantage +4.48 pp above the shuffled-label baseline and from Within's not at all, and the two rules still reach the same held-out score and action distribution inside each harness. Re-collecting half the training data on-policy does not change this. Cross-harness credit yields configuration adaptation and no more portable capability than within-harness credit. Multi-harness RL reports should state the grouping boundary and test under an unseen harness.

Reinforcement Learning from Verifiable Rewards works well when a task has a programmatic checker, but most long-horizon agent domains have none. We work in the outcome-blind setting, where ground-truth success signals are not available. Multi-criteria rubrics are a popular way to supply such a reward; they are scored once per trajectory, but a single scalar is a poor signal across tens of steps. We propose DRACO: Distributing Rubric-based Advantage for Credit Optimization. It generates rubrics dynamically during training to track the policy's evolving capability, scores those rubrics once per completed trajectory, and redistributes that judgment over the steps responsible for annotated rubrics to produce differentiated per-step advantages in GRPO. The redistribution is closed-form and does not introduce any trained attribution module. On AppWorld, DRACO gains 15.9 points over the base model and 5.3 points over GRPO trained with a sparse ground-truth reward, despite not using any verifiers itself. On out-of-domain Tau-Bench, it gains 5.3 points over the base model even without a frontier judge, beating both ground-truth-reward training and other rubric-based training settings. The code for DRACO is available at https://github.com/IBM/draco.

Graph-based policy optimization improves credit assignment for long-horizon LLM agents by organizing rollout trajectories into state-transition graphs. However, existing methods construct graphs independently within each policy update, discarding transitions discovered by earlier policies and limiting advantage estimation to small, batch-local rollout groups. We propose \emph{Temporal Instance-Graph Policy Optimization} (TIGPO), which extends graph-based credit assignment across policy updates. TIGPO maintains a persistent transition graph for each task, allowing valid transitions discovered by different policy versions to jointly determine credit for current rollouts. To actively reconnect current exploration with historical experience, TIGPO allocates a fixed rollout budget between Exploration slots for ordinary task sampling and Revisit slots for delayed reattempts of previously explored tasks. For each revisit, TIGPO pairs the current rollout group with its corresponding earlier Exploration group to construct a cross-temporal reference. The enlarged reference is designed to stabilize relative advantage estimation under small rollout groups, while comparison on the same task directly captures policy improvement across training stages. Historical transitions and scores serve only as structural and detached statistical references and are never replayed in the policy loss. Experiments on ALFWorld and WebShop demonstrate that TIGPO consistently outperforms prior group-based and graph-based policy optimization methods.

Reinforcement learning (RL) for search agents typically relies on outcome rewards. However, it often fails to achieve effective credit assignment, due to the unclear value of intermediate steps. It is hard to separate their contributions from the final result. In this paper, we propose a dense process supervision method based on fact utility estimation, which models the reasoning process as the accumulation of discrete evidence facts. We first extract structured facts from raw observations and organize them into an explicit fact store. To support credit assignment, we then cluster semantically equivalent facts and infer the posterior utility of each fact cluster using Bayesian estimation over group rollouts. Finally, we convert the estimated fact utilities into dense step-level rewards to guide RL training. Experiments on seven single-hop and multi-hop QA benchmarks show that our method consistently outperforms existing baselines. Ablation studies validate clear relative improvements on multi-hop QA compared to outcome reward-only training.

Interactive web application generation requires models to produce usable HTML, CSS, and JavaScript applications from natural language requests. Unlike conventional code generation, application quality depends on multiple user-facing functional requirements, each often tied to localized code regions such as event handlers, state updates, DOM fragments, or CSS selectors. Standard GRPO collapses these structured outcomes into a single sequence-level reward and applies the resulting advantage uniformly to all tokens, weakening credit assignment. We propose \textbf{Rubric-to-Code Credit Assignment} (RCCA), a reinforcement learning framework that converts rubric-level functional feedback into localized optimization signals over generated code. RCCA builds training tasks around explicit functional rubrics, uses a hierarchical reward to separate format, source-code, runtime, and functional failures, and aligns evaluator-generated textual attributions with responsible code spans and generated tokens. The resulting model, \textbf{Ling-RCCA-Flash}, scores 41.25 on MiniAppBench, improving Ling-3.0-Flash by 32.20 points and slightly surpassing Claude Opus 4.5. It also reaches 76.19 on ArtifactsBench, improving the SFT model by 4.48 points and establishing a new top score under the official ArtifactsBench leaderboard setting by surpassing the GPT-5 score by 3.64 points, suggesting transferable implementation-level gains.

Tool-Integrated Reasoning (TIR) is a fundamental capability for LLM agents to solve complex tasks by interacting with external tools iteratively. Reinforcement Learning (RL) has become the dominant paradigm for enabling this capability. However, existing approaches typically assign uniform trajectory-level advantages and treat all correct tool calls equally, ignoring the varying difficulty and learning value across trajectories and reasoning steps. This can lead to imprecise learning signals that do not adequately distinguish between trivial and challenging tool-use patterns. To address this limitation, we propose HiDiffTIR, a Hierarchical Difficulty-aware policy optimization framework for multi-turn TIR. HiDiffTIR performs difficulty-aware credit assignment at both trajectory and turn levels, enabling the policy to focus on more informative trajectories and harder reasoning steps. Notably, this fine-grained optimization is achieved without additional supervision, relying solely on group-level statistics derived from standard RL rollouts. Extensive experiments on three tool-using benchmarks demonstrate that HiDiffTIR consistently improves multi-turn TIR performance and tool invocation accuracy over strong RL baselines, highlighting the necessity of difficulty-aware credit assignment for effective policy optimization in tool-integrated LLM agents.

Training multi-turn agentic workflows with reinforcement learning (RL) enables large language models to perform complex reasoning, use external tools, and conduct iterative search beyond single-turn settings. Yet multi-turn RL training remains highly unstable, often causing severe performance degradation as the number of turns increases. Through theoretical analysis, we identify three tightly coupled sources of instability: rollout-training context mismatch, weak turn-level credit assignment under sparse terminal rewards, and asynchronous policy drift when short and long trajectories are optimized under different policy versions. We show that these issues share a common structural origin in flattened trajectory optimization and address them through a unified reverse-turn formulation. We propose Reverse-Turn Policy Optimization (RTPO), which organizes multi-turn rollouts as sparse reverse trees and performs turn-level policy updates in temporal reverse order, aligning each decision with its downstream continuation. RTPO enables causally consistent turn-level credit assignment and on-policy continuation to control asynchronous drift. We provide theoretical guarantees showing that RTPO eliminates context mismatch and asynchronous drift under the proposed turn-level formulation, reduces credit bias, and converges to recursive optimality. Experiments on multi-turn agentic RL benchmarks show that RTPO improves upon trajectory- and turn-level baselines by 21.50% and 10.76%, respectively, highlighting its potential to support more stable training for tool-using agents.

Reinforcement learning with verifiable rewards (RLVR) offers a verifier-bounded performance ceiling for training multi-turn tool-use agents, yet its trajectory-level credit assignment conflates heterogeneous per-turn outcomes into a single reward signal. On-policy distillation provides dense per-token supervision but is either teacher-bounded or prone to gradient concentration collapse. We introduce $\textbf{CrEST}$, a hierarchical credit assignment framework that retains RL's verifier-bounded ceiling while incorporating dense token-level signals from a privileged self-teacher. $\textbf{CrEST}$ resolves credit at two levels: turn-segmented verified advantages address inter-turn dilution, while entropy-gated self-teacher modulation refines intra-turn token contributions. Experiments on BFCL V3 and WildToolBench show that $\textbf{CrEST}$ consistently outperforms both RL and distillation baselines across two model scales, with the largest gains on long-trajectory and strict session-level metrics. Our work demonstrates that the teacher's role in policy optimization can be reduced from determining update directions to modulating update magnitudes, unlocking dense credit assignment without sacrificing the verifier-bounded ceiling.

Semantic-ID generative recommenders represent each item as a short sequence of discrete semantic tokens and predict the next item by autoregressively generating this token sequence. This paradigm enables a unified generation interface for item IDs, histories, and item text, but it also creates a structured optimization bottleneck during reward-based post-training: when an early semantic token enters the wrong branch of the item-token space, finite rollout groups rarely reach the ground-truth item, so group-relative optimization receives identical zero rewards and produces no useful advantage. We propose Hint-Conditioned Generative Recommendation (HCGRec), a semantic-ID generative recommendation framework that recovers learning signal for such hard training instances. HCGRec diagnoses each instance with checkpoint rollouts and supplies a minimal target-prefix hint only when the current generator cannot reach the correct item. The model then generates the unhinted suffix under the hinted semantic branch, turning zero-reward groups into informative comparisons over item-token completions. Hinting also changes token identity: hinted prefix tokens are oracle-provided item context, while unhinted suffix tokens are sampled generation actions. We therefore introduce hint-aware credit decomposition, using supervised learning to preserve item-semantic and prefix-structure alignment for hinted tokens and GRPO to optimize the sampled suffix. Experiments on sequential recommendation benchmarks show that HCGRec substantially improves over supervised fine-tuning and vanilla reward-based post-training, while reducing zero-advantage training samples from over 70% to below 20%. The code is accessible at https://github.com/WncFht/GRec.

Financial institutions are delegating consequential decisions to agentic AI systems that decompose goals, coordinate models and tools, and act with little oversight. Yet agentic AI governance in FinTech is under-investigated. We argue the binding governance constraint is not capability but verifiability. We define the Verifiability Gap as the shortfall between the verification delegated authority demands and the explainability and reproducibility retained after a decision. It is indexed to a verifier, evidentiary standard, and audit lag. We develop a multilevel governance theory for agentic AI and test its mechanisms in three studies over nine model versions, from a three-billion-parameter local model to a commercial frontier system. Study 1 shows that provider releases alter historical financial actions, and that the controls replay needs belong to the provider: the frontier model rejects temperature, top_p and top_k outright and exposes no random seed. Under the tightest controls each endpoint allows, a local model reproduced 320 of 320 executions, hosted models 319 of 320 and 959 of 960. Study 2 shows that orchestration is a latent policy layer. Architecture changes final actions, and no execution record repeated in any configuration at any scale. The frontier model reproduces its own actions more often than the local ones, its record no better, and loses a comparable share of its differentiation. Capability buys a higher starting point, not auditability. Study 3 shows two deterministic credit-model versions each reproduce their current action perfectly, yet the current cannot recover a historical one. We conceptualize reproducibility as a governance profile, not a scalar, yielding evidence-contingent delegation: authority is defensible only while retained evidence substantiates its exercise. Beyond finance, the framework extends to other high-stakes domains requiring auditability.

Recent advances in video generation models have significantly improved the realism of synthetic videos, blurring the boundary between generated and authentic content and raising concerns about misinformation. Existing MLLM-based detectors mainly rely on supervised fine-tuning or label-level reinforcement learning, where coarse supervision limits generalization to unseen scenarios and emerging video generators. To overcome these limitations, we are the first to introduce \textbf{meta-detection} into AI-generated video detection, enabling reliable forgery detection by jointly optimizing predicted labels and supporting evidence within reinforcement learning. This paradigm requires reliable evidence signals and effective mechanisms to integrate them into label-level optimization. Textual rationales provide semantic descriptions of forgery artifacts, but their generation and verification depend on external models, making supervision vulnerable to hallucinations and semantic biases. In contrast, temporal grounding provides more objective and verifiable evidence, as manipulated intervals can be precisely controlled during forgery construction. Based on this insight, we propose an automated data construction pipeline that generates paired real-fake videos by replacing temporal segments with boundary-frame-conditioned video generation models. Furthermore, we introduce \textbf{Evidence-Guided Reward Redistribution}, which performs evidence-aware credit assignment by redistributing rewards among label-correct responses according to evidence quality. This preserves reliable label supervision while encouraging detectors to acquire fine-grained and verifiable forgery localization capabilities. Extensive experiments demonstrate that \textbf{VidForensics-M1} effectively leverages verifiable temporal evidence to achieve robust and generalizable AI-generated video detection.

Direct Preference Optimization (DPO) aggregates token-level log-probability ratios via uniform summation, implicitly treating all tokens as contributing equally to the preference signal. However, the contribution of individual tokens to the preference signal varies. We introduce token credit, which modulates each token's KL regularization based on its contribution to the preference outcome. We derive that effective token credit is proportional to the magnitude of each token's implicit reward, and observe that this quantity evolves substantially during training. This implies that static token credit becomes increasingly misaligned as training progresses. In this work, we propose Se-DPO (Self-Evolving Token Credit for DPO), a live mechanism that derives token credit from the model's own evolving internal signals during DPO training. Since the reward signal varies in reliability across positions, Se-DPO calibrates token credit based on both the strength and the confidence of each token's contribution. Se-DPO requires no external models, adding only a lightweight calibration network with minimal computational overhead. Experiments show that Se-DPO improves over DPO by up to 9.8 points on AlpacaEval~2 and 12.2 points on Arena-Hard.

Agentic reinforcement learning (RL) often suffers from delayed and sparse rewards in real-world environments. A promising solution to this challenge is credit assignment, which aims to decompose trajectory-level rewards and provide more fine-grained supervision for intermediate decisions. However, existing credit assignment approaches ignore the rich process information naturally generated during environment interaction, e.g., interaction history. We argue that such information provides valuable supervision for identifying the contribution of individual actions. To this end, we propose Environmental Feedback-based Credit Assignment (EFCA), a multi-timescale credit assignment approach for long-horizon agentic RL. EFCA complements the long-term outcome signal with two environment-grounded process signals: a short-term feedback signal that captures the immediate effect of the current action and a medium-term state-history signal that identifies ineffective patterns from recent interactions. Both signals are directly extracted from environment feedback and integrated through a return reweighting mechanism. Experiments on ALFWorld and WebShop demonstrate that EFCA consistently improves both task success and task quality over strong baselines, highlighting the effectiveness of environment-grounded multi-timescale credit assignment for long-horizon agentic RL.

Offline reinforcement learning repeatedly trains policies from a fixed transition pool, making redundant data costly across seeds and hyperparameters, while naive subsampling can remove rare transitions needed for long-horizon credit assignment. We introduce CODS, a critic-guided selector that alternates between fitting an algorithm-matched critic and acquiring high-residual transitions before freezing a reusable subset. Unlike prioritized replay, CODS produces a static artifact; unlike one-shot residual selection, it refreshes scores as the critic changes. At a 10% budget, CODS retains 96.6% of eligible-pool performance across 20 valid D4RL task--algorithm cells. It exceeds ReDOR and OPER on 19/20 cells and every other subset baseline on 20/20; all six subset advantages remain significant under predeclared hierarchical inference with Holm correction. Holding total selector updates fixed, five acquisition rounds improve four representative cells by 11.23 points over one round and saturate thereafter. Equal-pass and equal-hour evaluations clarify that reuse, rather than a single-run speedup, creates the compute advantage. Mechanism and corruption interventions expose both useful sparse-reward enrichment and sensitivity to outliers. Finally, a whole-trace extension retains 95.4% of pooled ALFWorld success and 96.5% of pooled GSM8K exact match. CODS is therefore a reusable selection procedure, not a formal coreset guarantee.

Reinforcement learning with Verifiable Reward (RLVR) has emerged as a powerful paradigm for training coding agents, where the execution feedback from compilation and tests provides objective verification. However, unlike agent tasks, coding agents face a unique and finer-grained credit assignment challenge: at each step, coding actions simultaneously pack varying changes into different regions of a code version, which makes the contribution of independent change indistinguishable. Existing RLVR methods mostly leverage the outcome reward or step-level reward, which fails to dive into a code diff and makes unique properties of coding actions invisible to training. In this paper, we propose Diff-in-Diff Policy Optimization (DiDPO), a critic-free RL method that constructs fine-grained credit units directly from the structure of code diffs. DiDPO organizes multi-turn coding interactions into multiple thought--action steps and discovers code diffs across sampled trajectories. It then selects anchors by aggregating highly similar sub-diffs split from each whole diff by our ``groupability score'', which provides the splitting schema that optimally balances the semantic scope of anchors and the group mass they may form. Finally these anchors form advantage groups and project the diff-level advantage back to individual response tokens. Experiments on long-horizon coding and reasoning benchmarks show that DiDPO significantly outperforms strong agentic RL baselines. On Qwen2.5-7B-Coder, DiDPO exceeds comparable methods by over 10% and narrows the gap with far larger models, offering a principled framework for fine-grained credit assignment in coding agent training. We also open-source verl-code, an agentic rl codebase that supports various RL methods and coding benchmarks.

Credit assignment in multi-turn agent reinforcement learning operates at two levels: assigning trajectory-level credit to actions and distributing each action's credit across its tokens. In this paper, we introduce FACTOR, which separates these decisions. FACTOR uses checkpoint-calibrated TD residuals to assign per-action credits that telescope to the trajectory advantage, and feedback-conditioned teacher-student likelihood gaps to allocate each credit across the realized action tokens. Per-action normalization preserves the action-average coefficient and prevents token-level sign flips. We pair this construction with an action-mean reduction, removing the implicit dependence of an action's scalar surrogate weight on its token length. At the behavior policy and before clipping, each action's inner action-mean surrogate equals its TD credit. FACTOR consistently improves over competitive baselines across ALFWorld, WebShop, and ScienceWorld, with every environment-seed comparison favoring FACTOR and the largest gains emerging on the longest-horizon environment. The same hyperparameters transfer without retuning to a larger backbone and to a different model family. Ablations identify TD action credit as the dominant driver of the improvement, with hindsight token allocation contributing complementary gains.

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.

Reinforcement learning (RL) with verifiable rewards constructs trajectory-level advantage estimates, yet it often fails to credit the few pivotal decisions that determine outcomes in long-horizon, multi-turn agentic tasks. Recent work introduces privileged self-distillation for credit assignment, providing denser supervision, but it remains unclear how such local signals should represent sequential credit. We propose AgentOPSD, a critic-free, recursive method for turn-level credit assignment in agentic reinforcement learning. AgentOPSD aggregates token-level teacher-student log-probability gaps into turn-level evidence and recursively updates a Bayesian belief state in log-odds space. This yields a principled reweighting scheme that converts sparse outcome supervision into turn-level credit signals and identifies pivotal turns through the marginal belief revision between consecutive states. The method is fully compatible with standard policy optimization and requires neither an additional critic nor extra rollouts. We evaluate AgentOPSD on ALFWorld, WebShop, and Search-QA using Qwen2.5 models at two scales (3B and 7B). AgentOPSD outperforms GRPO and strong self-distillation baselines, achieving 89.1% success on ALFWorld with Qwen2.5-7B. Ablation studies attribute the gains to turn-level aggregation and history-dependent recursive belief updates.

Long-horizon search agents must make multiple sequential actions (steps) to search, retrieve, verify, and integrate evidence to reach a final answer. However, existing methods for training these agents typically treat all steps within a trajectory uniformly during both supervised fine-tuning (SFT) and reinforcement learning (RL), failing to distinguish useful actions from erroneous or redundant ones. In this paper, we propose Answer-Backtracked Credit Assignment (ABC), a fine-grained credit assignment framework for training long-horizon search agents by converting sparse trajectory-level outcomes into dense step-level supervision that rewards useful actions (even in failed trajectories) while suppressing erroneous or redundant actions. Specifically, given a potentially obscure query and its corresponding ground-truth answer, ABC first performs Answer-Backtracked Clue Recovery, which traces back from the answer to recover intermediate clues required to solve the question. It then applies Clue-Anchored Step Scoring to evaluate each search step against these clues, converting sparse binary outcome supervision into dense step-level rewards. Based on these rewards, we develop ABC-SFT, which reweights the loss of each turn, and ABC-GRPO, which uses the step-level scores as rewards in GRPO. Building on this framework, we train ABSeeker based on Qwen3.5-4B with only 8.5k examples. ABSeeker achieves 37.3% on BrowseComp and 39.1% on BrowseComp-ZH. With context management, the scores further improve to 55.3% and 52.9%, respectively, significantly outperforming same-scale (4B) agents and even matching the performance of larger ones (approximately 30B). These results demonstrate the effectiveness of answer-backtracked step-level credit assignment for training long-horizon search agents.

Reinforcement learning with verifiable rewards (RLVR) com- monly optimizes each correct completion as an independent learning signal. In GRPO, this completion-level uniformity creates structure-level skew: recurring correct solution forms accumulate positive coefficient mass in proportion to how often they are sampled, while rare forms receive limited credit. We formalize this behavior as multiplicity-induced structure-level credit concentration and introduce a partition- conditioned rule that redistributes positive advantages accord- ing to cluster rarity. Cue-GRPO instantiates this rule with- out auxiliary-model inference by using deterministic Strategy Cues to construct rollout-local partitions of verified-correct traces. Across Qwen2.5-Math-7B and Llama-3.1-8B-Instruct, Cue-GRPO improves AIME repeated-sampling performance, with the largest gains at high sampling budgets. Credit Re- distribution (CR) under Judge Partitions (JP) further indi- cates that the proposed redistribution mechanism can oper- ate with judge-derived partitions. Cue-GRPO adds only 6% wall-clock training overhead over GRPO. These results sup- port structure-level credit redistribution as a practical design axis for RLVR, with Strategy Cues providing a low-overhead implementation for competition mathematics. Code is avail- able at https://github.com/CzZ12/When-Correct-Solutions- Repeat-Rarity-Aware-Credit-Redistribution-for-GRPO.

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

Parameter-efficient post-training reduces the number of trainable parameters, but still requires repeated end-to-end backpropagation through the frozen backbone. Every adaptation step therefore needs backward-capable hardware and must store or recompute activations. We ask whether this repeated backward chain can be replaced by a one-time calibration. We introduce Local Credit Assignment (LoCA), a two-stage method for small-shift adaptation. One probe backward pass fits a low-rank map at each transformer block from the final prediction error to a local hidden-state correction. LoCA then reuses these maps to form blockwise regression targets from forward activations and fits low-rank adapters with closed-form ridge solves. No further backbone backward pass is required. We evaluate LoCA on five discriminative benchmarks with Qwen2.5 models from 0.5B to 14B. In 16 of 25 reported task--scale comparisons, LoCA yields lower evaluation cross-entropy than the corresponding LoRA run. Its measured full-run GPU peak, including calibration, is 26--29% lower than LoRA's. After calibration, its CPU steady-state memory is 36--52% lower and its per-pass time is 43--48% lower. A shared scale-normalized candidate set is reused across all tested Qwen2.5 sizes and on SmolLM2-1.7B. LoCA thus amortizes global credit assignment into one calibration and enables later forward-only tuning when repeated backpropagation is impractical. The code associated with this paper is available \href{https://github.com/Xia12121/LoCA}{here}.

Optimization-based latent reasoning improves large language model outputs by optimizing instance-specific continuous states at test time while keeping model parameters frozen. Existing methods, however, typically connect these states to the reasoning trajectory through decoded tokens, making sequence-level credit assignment indirect and obscuring how latent updates shape subsequent reasoning. We introduce GradCuit (gradient through circuit), which inserts optimizable latent states at a selected Transformer layer between the hidden representations of the prompt and the generated continuation. Causal self-attention provides every continuation-token log-probability with a differentiable path to every preceding latent state through the remaining Transformer blocks, enabling reward-weighted gradients from the entire continuation to be assigned directly to the latents. Across five instruction-tuned backbones, three reasoning benchmarks, and two answer formats, GradCuit achieves an average accuracy of 64.5%, outperforming chain-of-thought prompting by 6.6 percentage points and the strongest competing method by 2.4 points. GradCuit also demonstrates greater robustness: across seven learning-rate settings, it consistently outperforms LatentSeek while reducing the standard deviation of accuracy from 1.53 to 0.82, and even its random-walk variant remains competitive with LatentSeek. For interpretability, token-level gradient attribution reveals that latent influence concentrates on reasoning-connector tokens, while layer analysis identifies early-to-middle Transformer layers as the most effective optimization space. By directly optimizing internal reasoning from outcome feedback, GradCuit opens a new axis of robust and interpretable test-time scaling, where LLMs adapt how they reason rather than merely regenerate, sample, or rerank outputs.

Multi-agent reasoning (MAR) improves reasoning reliability through iterative solution exchange and refinement. Existing adaptive MAR methods typically learn routing decisions from query-level labels or trajectory-level returns, but such coarse supervision cannot accurately estimate the state-conditioned utility of individual operators in multi-step collaboration. We propose TreeCredit, a shared-prefix credit assignment framework for efficient adaptive MAR. Its core insight is to estimate operator utility through state-matched downstream comparisons, rather than directly attributing trajectory-level outcomes to preceding decisions. TreeCredit constructs shared-prefix collaboration trees by expanding candidate operators from the same intermediate state and assigns each state--operator pair a correctness-prioritized suffix credit based on the terminal correctness and cumulative additional cost of its complete continuation. These structured credits are converted into state-local operator preferences to train a lightweight pairwise state router, which dynamically selects the next admissible operator during inference. Experiments on six reasoning benchmarks show that TreeCredit modestly improves accuracy while substantially reducing inference cost, achieving a better accuracy--cost trade-off than representative MAR methods.

Verifier-guided reinforcement learning has become a powerful paradigm for improving LLM reasoning. In multi-turn settings, models receive a verifier score after each turn and iteratively refine their outputs. Although such scores provide dense feedback, they do not directly provide dense credit: a score measures the quality of the current output, while credit should measure how the current turn changes the refinement trajectory. We propose TCPO, a turn-level credit assignment method for verifier-guided multi-turn RL. TCPO casts credit assignment as score-to-credit conversion and constructs turn-level advantages through reference-based comparisons: retrospective credit captures immediate progress and regression relative to the best prior state; hindsight delayed credit identifies non-improving turns with later payoff; and selective fixed-history counterfactual estimation refines high-surprisal turns under the same history. Experiments on math reasoning, code generation, and AppWorld agent tasks show that TCPO improves or matches the strongest baselines across model scales, task domains, and verifier types. TCPO achieves the best or tied-best best-turn Pass@8 on Qwen3-4B and DeepSeek-R1-Distill-Llama-8B, reduces turns to success, and improves multi-turn agent performance. These results highlight score-to-credit conversion as a central ingredient for verifier-guided multi-turn policy optimization.

Latent reasoning allows language models to carry out intermediate reasoning in continuous latent representations rather than fully externalizing it as discrete chains of thought. However, assigning credit to such latent thoughts from answer-only rewards is difficult: a single final answer mixes thought quality with answer-sampling noise. We propose \textbf{Latent Thought Credit (LTC)}, a hierarchical credit-assignment framework for latent reasoning. For each prompt, LTC samples multiple latent thoughts, fixes the context after each thought, and estimates thought-level expected reward by averaging rewards over multiple answers generated from that fixed context. LTC uses thought-level advantages to optimize the latent-thought phase, answer-level advantages to optimize the answer phase, and an advantage-weighted thought-matching objective that helps the policy reproduce high-credit latent thoughts. We instantiate LTC in a GRPO-style on-policy training framework and evaluate it across mathematical reasoning and STEM multiple-choice tasks. LTC achieves the best average accuracy among the compared methods, while ablations and fixed-context diagnostics show that multi-answer estimation reduces reward-estimation error and mitigates ambiguous or incorrect thought-level credit.

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.

The rapid development of Large Language Models (LLMs) has opened new avenues for Automated Heuristic Design (AHD) for solving NP-hard combinatorial optimization problems (COPs). However, existing LLM-driven AHD methods are largely confined to rigid solver templates, relegating the search process to isolated module tuning. Transitioning to fully autonomous, system-level algorithm design is essential but fraught with low reliability of generated operators, extremely large search spaces, and ineffective credit assignment. To overcome these drawbacks, this paper proposes a Directed Graph-Guided Automated Algorithm Design framework, termed DGA$_2$D. It structures the open-ended program space as a directed graph, where each node represents a functional operator that can be instantiated using one of multiple candidate code implementations, while directed walks constitute complete algorithmic pipelines. A first-order path-dependent credit assignment mechanism is introduced to evaluate code variations strictly based on their topological context. Extensive experiments across 12 distinct COPs, ranging from complex scheduling to routing, demonstrate the consistent empirical advantages of DGA$_2$D. It reduces the average normalized gap by up to 10.96 percentage points compared to state-of-the-art LLM baselines.

Recent advances in image generation and editing have made prompt quality a key bottleneck for e-commerce creatives. Vision-language models (VLMs) can generate image-editing prompts from product images and metadata, but further improving their prompt-writing capabilities requires post-training with feedback from the generated images. Group Relative Policy Optimization (GRPO) is a natural framework for such outcome-level reward optimization. However, it assigns credit only at the full-prompt level, even though image quality often depends on specific design elements such as composition, background, and the presentation of selling points. Existing fine-grained credit assignment methods typically require step-level supervision or learned critics. To address this, we propose EAGLE-GRPO (Element-Aware Group Learning for E-Commerce Image Generation), which decomposes the group-centered reward over predefined elements. We cast element-level credit assignment as a kernel ridge regression problem and derive a closed-form solution, without additional rollouts or separate credit-assignment models. This yields interpretable per-element advantages and more precise policy updates. Experiments show that EAGLE-GRPO sustains performance gains over more training steps before plateauing and generates prompts that produce higher-quality e-commerce images than competitive VLM prompt-writing baselines.

Multistep credit assignment is critical for sample-efficient reinforcement learning, yet managing off-policy bias in Q-learning remains a fundamental challenge. For 30 years, practitioners have been limited to a binary choice: eliminate the bias at the cost of severely truncated eligibility traces (Watkins' Q($λ$)), or ignore the bias to learn faster while injecting detrimental errors into the value estimates (Peng's Q($λ$)). Modern off-policy estimators fail to resolve this tension, as importance-sampling ratios collapse under Q-learning's greedy target policy. We introduce Gated Q-learning, a novel algorithmic framework that ends this dilemma by smoothly interpolating between the two historical extremes. Rather than relying on importance sampling, our approach employs a continuous, state-action-dependent gating mechanism to selectively attenuate eligibility traces in an exploration-aware manner. We provide a rigorous theoretical foundation for this mechanism, proving that the expected operator remains a contraction mapping and deriving its exact fixed point. Empirical evaluations verify that intermediate gating safely enables longer credit-assignment horizons, yielding faster initial learning than either extreme. Gated Q-learning offers a simple alternative to importance sampling while enabling customization of the effective multistep horizon and the amount of off-policy bias in Q-learning agents.

On-policy distillation provides dense supervision for multimodal reasoners, but its trajectory-level reward cannot determine whether a failed answer arose from perception or subsequent reasoning. Perception Success Rate (PSR), estimated from multiple reasonings sharing one perception, remains ambiguous because low success conflates perceptual insufficiency with reasoning difficulty. We introduce \textbf{Perception-Correction Distillation (PCD)}, a label-free method that identifies correctable perception failures using downstream failure and teacher--student disagreement as complementary witnesses. Their product, , forms a soft AND gate that strengthens distillation only when both witnesses are present. We motivate this rule through Bayesian evidence combination and show that multiplication is the unique normalized bilinear gate that vanishes when either witness is absent. PCD uses separated perception--reasoning rollouts and mean-preserving weights, leaving the reasoning objective unchanged. Across eight benchmarks, PCD improves the 8B 2B macro average from 44.50 with OPD to 47.28 and the 32B 8B result from 56.94 to 61.22. In matched 2B ablations, removing PCD and separated rollout reduces held-out average by 2.22 and 0.88 points, respectively. Effective multimodal distillation therefore depends not only on what the teacher predicts, but also on identifying when perception is the appropriate target of correction.

Credit assignment is a fundamental challenge in cooperative multi-agent reinforcement learning, particularly in embodied AI settings characterized by limited and delayed feedback as well as dynamically changing numbers of active agents. We propose MARS-RA, a framework that reformulates credit assignment as a rank aggregation problem using contribution-based pairwise comparisons among agents generated by large multimodal models. This shift from absolute to relative estimation ensures robustness against noise and dynamic agent participation, converting comparison results into contribution scores for potential-based reward shaping. We provide theoretical justification for the convergence and robustness of the proposed framework, and show that Shapley values can be used as an interpretive reference. Experimental results on challenging tasks of different types indicate that MARS-RA can guide agents toward effective cooperation.

Reinforcement learning with verifiable rewards (RLVR) is central to improving long-CoT reasoning in large language models. Critic-free methods such as GRPO convert response-level rewards into advantages and uniformly broadcast them across tokens, overlooking their unequal contributions to the final outcome. On-policy self-distillation (OPSD) instead provides dense distributional supervision by minimizing the forward KL divergence between an unprivileged policy and a privileged self-teacher, implicitly assuming that the resulting likelihood shifts encode reliable answer-aligned information. We test this premise by fixing each sampled trajectory and re-scoring it under two opposing outcome conditions, one asserting correctness and the other incorrectness. Most affected tokens shift in the same direction under both conditions, with few sign reversals and substantial overlap in the induced optimization signals. Large shifts also concentrate on highly substitutable surface-form tokens, whereas tokens carrying problem-specific reasoning content are less sensitive. These findings show that privileged shifts fail to provide reliable answer-aligned directions, while their magnitudes primarily reflect counterfactual sensitivity rather than token-level learning value. Based on these observations, we propose Counterfactual Sensitivity Credit Reallocation (CSCR), a simple extension of GRPO that reduces credit for highly sensitive tokens and renormalizes token-level advantages to preserve both the original credit budget and verifier-determined direction. On long-CoT mathematical reasoning benchmarks, CSCR consistently outperforms GRPO baseline with the same number of policy updates. Targeted ablations further corroborate our diagnosis: privilege-induced directions are unreliable, moderate downweighting is most effective, and stronger modulation destabilizes optimization.

Reinforcement learning (RL) search agents commonly model retrieval as free-form natural-language query generation and optimize multi-turn interactions using final-answer rewards. Current studies mainly improve training with denser or more structured credit signals, but rarely examine whether retrieval is properly formulated at the policy-environment interface. We observe pronounced retrieval aliasing during Search-R1 training: rollouts for the same question continue to generate distinct query strings, yet their accumulated evidence sets increasingly overlap. We call this phenomenon retrieval-equivalence collapse; in this regime, trajectories approach utility equivalence with respect to retrieval decisions, leaving within-group returns with little effective retrieval contrast. To address this problem, we propose Harness-G, a graph-structured retrieval framework that redesigns this interface. It reformulates free-form query generation as finite action selection: the policy selects an evidence sentence or entity, or chooses to answer, while the environment constructs the menu, tracks retrieval state, and validates and executes each choice. This interface reduces linguistic aliasing and makes same-state alternatives directly comparable. Building on this interface, we introduce Structured Non-myopic Credit (SNC), which uses a frozen answer scorer to compare the selected action with its alternatives and assigns downstream gains to the earlier actions that enabled them. Across six QA benchmarks, Harness-G achieves the highest average F1 at both evaluated model scales, outperforming the strongest baseline, Graph-R1, by 10.74 points at 1.5B and 3.98 points at 3B.

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.

Rubric-based reinforcement learning enriches language model training by evaluating model outputs against explicit criteria. Yet in GRPO-style pipelines, these structured judgments are reduced to a scalar response-level reward and converted into a response-level advantage, which is broadcast uniformly to all generated tokens. This leaves no explicit mechanism for allocating credit within a response, even when different criteria are grounded in different spans, formatting decisions, or semantic choices. We propose CoRT, a token-level credit weighting method for rubric-conditioned GRPO. Instead of training an auxiliary token scoring model, CoRT uses counterfactual replay to rescore the same sampled response under the original rubric-conditioned prompt and a matched criteria-free prompt. The resulting tokenwise log-likelihood contrasts serve as a proxy for dependence on the rubric context. CoRT maps these contrasts to bounded, response-normalized weights and uses them to redistribute the signed GRPO advantage across tokens, without introducing an auxiliary scorer or changing the response-level reward. Experiments across instruction-tuned models and reward granularities show that CoRT improves over matched response-level GRPO in the vast majority of comparisons, with an average gain of 4.4 percentage points. The method remains competitive with learned token-level credit baselines while avoiding a separate relevance-learning stage. These results suggest that policy-internal counterfactual likelihood contrasts provide an effective training signal for within-response credit allocation while retaining the simplicity and stability of GRPO.

Effective memory is crucial for LLM agents, yet constructing it effectively remains challenging. A memory-construction policy decides what information to extract, store, update, compress, or discard as interactions accumulate. Heuristic memory methods rely on subjective, task-specific rules, which can misalign with downstream objectives and limit cross-task adaptability. RL-based methods, by contrast, learn from task feedback but mainly use outcome- or module-level rewards. These coarse signals indicate task success but cannot identify which intermediate memory contents support the final answer, creating a fine-grained credit-assignment bottleneck. However, constructing such process feedback is prohibitively difficult because intermediate memory decisions lack unique ground-truth targets, while the appropriate credit varies with the agent's uncertain reasoning trajectory and therefore cannot be specified in advance. We propose AttriMem, an attribution-guided process-feedback framework for learning memory-construction policies with RL. AttriMem augments the global outcome reward with local rewards derived from token-level contributions to the final answer. Experiments on long-horizon dialogue question answering show that AttriMem outperforms retrieval-based, heuristic, and RL-based baselines, generalizes across benchmarks and answer models, stabilizes RL optimization.

Personal and organizational planning systems maintain two records that drift apart: what was planned (a task's effort budget) and what was done (a logged action's duration and description). Existing systems bridge them with an exclusive, all-or-nothing link that strands genuinely related but unlinked effort and reports false stalls on active goals. We formulate the bridge as a quasi-linear Fisher market: planned tasks are budget-constrained buyers, performed actions are divisible goods, and a fused text/structural/temporal signal sets each buyer's valuation. Two market instruments - a seller reserve price and a buyer cash option - yield conservation, a hard budget cap, and a provable junk filter as theorems. We extend the market with a concave completion utility discounting progress as a task nears its plan; standard convergence theory for the market's algorithm does not transfer here, resolved by a satiation-threshold fixed point with existence (Brouwer) and local uniqueness under an explicit diagonal-dominance condition, validated empirically on random and adversarial instances. A de-circularized, multi-seed benchmark - observed affinity corrupted independently of the scored ground truth - surfaces a genuine weak spot: the market's sharp, zero-entropy equilibrium is more sensitive to affinity noise than entropy-regularized optimal transport's permanently smoothed one. We resolve this with a one-parameter entropy-regularized generalization unifying the two, plus a noise-adaptive rule for its regularization strength. We report full reproducibility parameters, discuss limitations candidly, and relate the result to multi-touch attribution, optimal transport, and online Fisher-market algorithms.

Critical infrastructures are increasingly distributed, interdependent, and exposed to evolving disruptions, making resilience a central requirement for their operation and control. This paper argues that decentralized multi-agent reinforcement learning (MARL) should be understood not merely as a distributed alternative to centralized training with decentralized execution but as a paradigm structurally aligned with the requirements of resilient critical infrastructures. This perspective is grounded in an analysis of the properties of decentralized MARL and the requirements of critical infrastructures, including scalability to large numbers of agents, support for privacy and local autonomy, robustness to failures, and interaction-driven adaptation among interdependent components. However, structural alignment alone is insufficient for practical deployment. This paper identifies credit assignment and communication as two central conditions for its practical feasibility. Credit assignment determines whether local learning remains aligned with system-level objectives, while communication determines whether coordination can be learned and maintained under realistic operational constraints. Building on these challenges, this paper proposes a research agenda focused on structure-aware, causality-aware, and resilience-aware credit assignment; communication for both coordination and credit assignment; and safe, timely, and recoverable decentralized learning under deployment constraints. Overall, this paper reframes decentralized MARL as a promising but conditional foundation for resilient critical infrastructures.

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.

Multi-turn agents solve complex tasks through extended sequences of tool interactions before producing a final answer, making credit assignment a fundamental challenge during post-training. Outcome rewards provide reliable supervision for short-horizon reasoning, but become sparse and high-variance as trajectories grow to tens or hundreds of tool calls. They can also be misleading: a failed rollout may contain many useful actions that move the agent closer to the goal, yet outcome-only training assigns them the same negative advantage as the eventual mistake. We propose TRACE (Turn-level Reward Assignment via Credit Estimation), a dense credit-assignment method for agentic reinforcement learning. TRACE represents rollouts as state transitions at tool-call boundaries, obtains gold-answer log-probabilities from a frozen reference model, transforms them into log-ratio state values, and derives per-action rewards as Temporal-Difference changes in those values. This requires no additional critic or process-label training, and its one-step log-ratio TD component telescopes across redundant tool calls. On long-horizon complex search, TRACE substantially improves base-model tool-use ability using pure RL, without a cold-start supervised fine-tuning stage, an agentic mid-training stage, or training on live-web data. On the closed-web BrowseComp-Plus benchmark, it raises Qwen3-4B from $7.2$ to $35.6$ and Qwen3-30B-A3B from $8.4$ to $42.6$. The learned search behavior also transfers to open-web benchmarks, and the learning curves show earlier improvement and faster convergence during RL training.

Reinforcement learning for deep-search agents has largely focused on trajectory-level scoring -- outcome correctness, citation-aware rewards, and evidence coverage. Yet the actions that expose supporting documents receive no targeted credit, a gap we call the reward-credit mismatch. We propose STAMP, in which a reference-based verifier judges whether each cited document supports an entity or relation in a training-time evidence graph, and first-exposure attribution traces each supported citation back to the action that first surfaced it. This step credit is injected through sign-preserving advantage modulation, which redistributes advantage across steps without changing the trajectory-level reward or the relative ranking of trajectories within each group. On BrowseComp, BrowseComp-ZH, and xbench-DS, STAMP improves the GRPO baseline by +2.0/+5.5/+3.0 points under matched SFT initialization, training data, and search tools, and composes with both outcome-only and citation-rubric base rewards. Component ablations confirm that the provenance-based credit signal and the sign-preserving advantage modulation each contribute to the gains.

Modern large language models (LLMs) operate in interactive multi-turn settings, making multi-turn jailbreaking a realistic threat model and an important setting for automated red teaming. A core challenge in learning multi-turn jailbreak attackers is credit assignment: different turns contribute differently to the final outcome, yet existing learning signals are often too coarse to identify their individual contributions. We propose decomposed credit GRPO (DC-GRPO), a unified turn-level credit assignment framework for Group Relative Policy Optimization in multi-turn jailbreak learning. DC-GRPO assigns a separate group-relative learning signal to each turn by combining immediate and future credit, avoiding the credit misassignment induced by broadcasting a single trajectory-level score across the dialogue. We instantiate this framework with static and dynamic weighting rules that differ in how the two credit sources are balanced while sharing the same turn-level structure. Across multiple victim LLMs and benchmarks, the dynamic- and static-weighted variants achieve average ASR5@3 scores of 98.26% and 97.88%, respectively, substantially outperforming the state-of-the-art methods, including SEMA (86.58%) and TROJail (86.23%). Their consistently strong performance indicates that the central empirical benefit comes from turn-level group-relative credit assignment rather than a particular weighting rule. Warning: This paper contains examples of harmful content.

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.

Reasoning language models frequently overthink: generating extended chains of behaviors such as hedging, approach abandonment, and self contradiction that consume tokens without improving answers. We show that these behaviors are not merely a consequence of length; even when controlling for response length, incorrect traces exhibit higher rates of unproductive self-reflection than correct ones. Addressing this requires identifying where self-reflection helps vs hurts, but obtaining these step-level annotations is costly. We observe that intermediate answer commitments within reasoning traces can provide a cheap proxy: by comparing each final answer candidate in the trace to the ground truth, we can determine whether subsequent reflection is productive without any additional supervision. Building on this insight, we propose DASH (Drift Aware advantage SHaping), which assigns segment-level credit based on whether each reasoning segment leads toward or away from correctness. On competition-level math benchmarks, DASH achieves the highest accuracy where overthinking is prevalent (AIME25: 50.8% vs. 45.4% GRPO) while reducing overthinking behaviors and achieving more productive self-correction than baselines.

Agentic reinforcement learning requires assigning credit to environment-facing actions such as searches, clicks, edits, navigation commands, and object interactions. Standard GRPO uses the final verifier outcome as a uniform advantage over all action tokens. This outcome signal is useful but structurally incomplete: it punishes useful exploration in failed rollouts and reinforces redundant or regressive actions in successful rollouts. We propose TRIAGE, a role-typed credit assignment framework that adds a semantic role axis to outcome credit. A structured judge classifies each segment as decisive progress, useful exploration, no-progress infrastructure, or regression, and a fixed role-conditioned rule maps these labels to bounded segment-level process rewards. This keeps verifier outcomes as the source of optimization direction while correcting the two main blind spots of outcome-only credit. We further show that role-conditioned credit is the optimal segment-level correction expressible from role labels alone -- a projection of the per-segment advantage residual onto the role variable -- so that the fixed role constants reduce advantage estimation error whenever the judge is reliable, and we connect this to lower-variance policy gradients. Across ALFWorld, Search-QA, and WebShop, TRIAGE improves success rates over GRPO for two policy models and outperforms both a scalar judge-derived process reward and an outcome-supervised shared-backbone value baseline. Ablations show that the gain comes from role typing rather than merely adding dense rewards: reliable detection of regression inside successful trajectories is the dominant contributor, while exploration credit provides a consistent secondary gain; on completed ALFWorld and WebShop rollouts, TRIAGE also reduces environment-facing turns by an additional $10.4\%$ and $14.8\%$ relative to GRPO.

Biological neural circuits obey Dale's principle: each neuron's synapses are uniformly excitatory or inhibitory. Artificial networks that respect this constraint must coordinate separate excitatory and inhibitory populations, fundamentally changing how credit is assigned during learning. Several biologically plausible learning rules avoid backpropagation's weight transport requirement, but it has been difficult to achieve strong performance under Dale's principle beyond MNIST. Error Diffusion (ED) was originally proposed in a dual-stream excitatory/inhibitory architecture, where learning is driven by routing global error signals to all layers without transporting transposed forward weights or relying on random feedback matrices. Whether such a rule can scale under Dale's principle across both supervised classification and reinforcement learning remains unknown. Here, we introduce modulo error routing to extend Error Diffusion beyond binary classification, and show that a dual-stream excitatory/inhibitory architecture trained with this method achieves 96.7% on MNIST and establishes a 61.7% baseline on CIFAR-10, demonstrating that representation learning is possible even when strictly enforcing Dale's principle. For the classification setting, we introduce three domain-specific innovations: layer-specific sigmoid widths, batch-centered class error signals, and asymmetric initialization, and ablation analysis reveals that their relative importance reverses between MNIST and CIFAR-10, exposing task-dependent credit-assignment bottlenecks invisible to single-benchmark evaluation. In reinforcement learning, we integrate ED with Proximal Policy Optimization (PPO) and evaluate it on continuous-control tasks in Google Brax and on Craftax, an open-ended exploration task. We show that ED-PPO achieves competitive performance relative to Direct Feedback Alignment, a backpropagation-free baseline.

Self-distilled agentic reinforcement learning augments trajectory-level reward with a token-level distillation loss, using as its teacher the same policy conditioned on privileged context. The prevailing recipe gates this loss by a single scalar, the teacher-student log-probability gap. This signal is doubly limited: it is retrospective, scoring only the realised rollout and never the counterfactual ones, and it is sign-blind, never signalling when a teacher-preferred action would have harmed the trajectory. We introduce CRAFT, a three-pillar credit-assignment scheme that addresses both limitations. Pillar 1, Counterfactual Token Importance, reuses the G-1 sibling rollouts that GRPO already samples and importance-weights them by the log-probability gap to form a self-normalised estimate of the group-level counterfactual change in advantage from up-weighting teacher-preferred actions at each step; this yields a signed per-token credit at near-zero extra compute. Pillar 2 is an asymmetric controller that raises the distillation weight as it lowers the reference-KL weight along an exponential moving average of gate activity, and conversely. Pillar 3 polarises the KL penalty token by token, switching between a mode-seeking and a mode-covering update according to the sign of the credit. Each pillar has an independent switch that, when disabled, renders the loss and gradient byte-identical to the baseline in IEEE-754 arithmetic, so any measured gain is attributable to algorithmic change rather than implementation drift. We prove the estimator's consistency and a variance bound, give structural and bit-exact reproducibility guarantees, and evaluate CRAFT across three agentic environments, four model scales, and five end-to-end methods, plus two tabulated prior-work baselines. Among these is Adaptive-CRINGE, a comparator sharing Pillar 2 with CRAFT, isolating the counterfactual contribution.

Group Relative Policy Optimization (GRPO) eliminates the learned critic in PPO by using the mean reward of grouped rollouts as a baseline. We provide a rigorous derivation of GRPO from first principles of the policy gradient theorem, revealing a fundamental credit assignment failure: under output-only reward, every token in a rollout receives identical advantage, collapsing token-level credit to a single scalar. We prove this induces gradient sparsity that intensifies over training, and demonstrate empirically via SVD analysis of GRPO gradients on Nemotron-4B/GSM8K that the gradient matrix has effective rank $\approx$ 2 regardless of group size $R \in \{2, 4, 8\}$. We formalize this as an intrinsic rank-2 structure arising from the zero-sum constraint on advantages and derive conditions under which GRPO's baseline is optimal. Our results characterize when GRPO's simplicity is theoretically justified and identify the credit assignment bottleneck as the key limitation for multi-step reasoning.

We propose a framework for reward allocation in fully delegated AI cooperatives where humans are represented by agents that contribute data and participate in model updates under heterogeneous value constraints. The key idea is to credit only those updates that remain admissible after screening them against each principal's value profile. We formulate value-conditioned gradient filtering, online marginal contribution signals, and cumulative revenue settlement within a traversal learning (TL) substrate. TL is especially attractive here because it performs decentralized backpropagation without the quality loss associated with aggregation-centric distributed learning and, we argue, offers a finer attribution substrate than FedAvg-style federated learning by preserving explicit traversal and gradient paths. The framework is positioned against data valuation, federated contribution estimation, personalized federated learning, and pluralistic alignment.

Multi-agent systems (MAS) built on large language models (LLMs) provide a promising framework for solving complex tasks through role specialization and structured interaction. However, their performance is often limited by miscoordination and, more fundamentally, the lack of fine-grained credit assignment across agents. Existing approaches typically rely on coarse-grained feedback, making it difficult to identify which agents or interaction steps are responsible for errors. We propose Gradient-Based Connections (GBC), an approach for fine-grained attribution and optimization of multi-agent systems. GBC models a MAS as a computational graph and introduces gradient-based connection weights to quantify the influence of each agent's output on downstream agents at the token level. By constructing an attribution graph and propagating task-specific loss signals backward, our method enables precise identification of error sources and targeted prompt optimization. We further develop AgentChord, an efficient implementation that leverages prefix-based gradient computation. Experiments on MultiWOZ and τ-bench show that GBC improves multi-agent performance and outperforms strong single-agent and multi-agent baselines, and higher attribution quality is associated with greater optimization effectiveness. Code is available at: https://github.com/yxc-cyber/AgentChord.

Process reward models (PRMs) enhance the reasoning capabilities of large language models (LLMs) by providing fine-grained feedback, yet training PRMs typically requires expensive stepwise annotations. Outcome-supervised PRMs offer a scalable alternative by learning from final-answer correctness alone, but this introduces a fundamental credit assignment challenge, i.e., attributing outcomes to responsible reasoning steps. Existing approaches rely on either uniform or causal assignment, both of which fail to anchor credit in step correctness and thus hinder process error identification. In this work, we propose Outcome-Supervised Process Reward Modeling via Learnable Credit Assignment (LCA), an outcome-supervised PRM framework that jointly learns credit assignment and reward modeling under the principle of Weakest Link Assignment: a reasoning chain is as strong as its weakest link. To address mutual dependence between credit assignment and reward modeling, we formalize outcome-supervised PRM as a Multiple Instance Learning (MIL) problem and introduce Softmax-Weighted-Sum (SWS) pooling, an MIL pooling technique tailored for strong dependence and redundancy among reasoning states. We prove Bayes consistency of our algorithm under mild assumptions. Extensive experiments demonstrate that LCA consistently outperforms state-of-the-art outcome-supervised PRMs across multiple tasks and backbones. Code is available at https://anonymous.4open.science/r/LCA.

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.