Dense Reward RL

The integration of graphs with Goal-Conditioned Hierarchical Reinforcement Learning (GCHRL) has received increasing attention, as graphs naturally encode task hierarchies for effective subgoal sampling. However, existing methods often overlook intrinsic connectivity information, failing to fully leverage the underlying topology for efficient learning. Most graph-based GCHRL methods use the graph as a stochastic sampling tool rather than as an environmental model that encodes connectivity and state-accessibility information. This limitation is particularly acute in quasimetric environments, where the inherent asymmetry of state transitions poses a fundamental challenge to stable policy learning and robust path planning. In this paper, we address these problems by introducing a state connectivity model designed to predict pairwise state connectivity strength in asymmetric environments. We transform these connectivity strengths into scalar auxiliary dense rewards, providing continuous guidance across multiple hierarchical levels. We demonstrate that our proposed framework, Graph-Guided Quasimetric Dense Reward (G2QDR), can theoretically be integrated into any existing GCHRL architecture, and the state connectivity model is efficiently implemented via a neural network trained on a directed state graph generated during exploration. Empirical results across a wide range of sparse reward environments indicate that, in general, G2QDR can enhance the performance of baseline GCHRL approaches with acceptable computational overhead.

Current paradigms for training language models via reinforcement learning rely heavily on sparse outcome rewards. However, as we pursue tasks that require longer and more complicated trajectories, such strategies result in slow learning. Prior work has attempted to address this problem by rewarding partial progress; however, naive formulations are often biased and converge to suboptimal policies. We show that a simple and unbiased dense reward formulation, which we term progressive point matching, scales exponentially more efficiently to long-horizon tasks by rewarding partial progress on a segment level, both theoretically and empirically via synthetic environments. We then show how progressive point matching can be practically instantiated using a single reference trajectory per task. On extremely hard math reasoning problems, sparse outcome rewards cannot make any progress, whereas segment-level rewards enable improvements at larger test-time token budgets when measured by success rate or pass@k.

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.

Reinforcement learning is a natural post-training paradigm for code-oriented large language models because generated programs can be evaluated through parsing, execution, unit tests, and structural analysis. However, existing methods often rely on sparse outcome rewards or statically combine heterogeneous dense signals, even though syntax validity, executability, functional correctness, and structural organization describe different and progressively dependent programming capabilities. We propose DHRCL, a reinforcement learning framework with Dense Hierarchical Rewards and Curriculum Learning. DHRCL decomposes feedback into syntax validation, execution success, unit-test pass rate, and AST-based structural similarity, and organizes these signals through a three-stage Syntax, Execution, Pass & Structural curriculum. Stage duration is determined automatically from recent validation trends rather than manually specified capability thresholds. We further introduce stage-aware probability-based token credit redistribution. The mechanism follows a consolidation-to-refinement principle: it emphasizes established token patterns during syntax-oriented optimization, applies uniform propagation for non-local execution feedback, and allocates more credit or blame to less-established token decisions during final functional optimization. Under a unified Qwen3-8B and KodCode protocol, the experiments compare DHRCL with binary, pass-rate, reward-model-based, and verifiable dense-reward baselines. We further evaluate DHRCL across Qwen3-4B, Qwen3-8B, and Qwen3-14B backbones, showing that its advantage remains consistent as model capacity increases.

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.

We suggest using the Lyapunov characteristic exponent (LCE) as a dense reward signal for the reinforcement learning problem of stabilizing the inverted pendulum with vertical motion. With LCE, the agent not only successfully found the oscillatory motion known as the Kapitza pendulum but also damped the pendulum's pivoting, leaving it in a strictly upright position.

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 long-horizon robotic manipulation is often limited by sparse and delayed rewards, while manually designing dense shaping signals is costly and brittle to changes in environments and object configurations. This work proposes Stage-Transition Dense Reward (STDR), a visual reward-learning framework that converts unstructured expert videos into logically grounded dense rewards for training RL agents from scratch. STDR leverages semantic understanding to infer a task's stage structure from demonstrations, and delivers two complementary learning signals during online training: (i) stage-transition feedback that provides goal-directed reward, and (ii) within-stage progress feedback that supplies fine-grained guidance toward completing each stage. Furthermore, an out-of-distribution (OOD) detection mechanism and a grasping regulation module are integrated to enhance robustness and prevent reward hacking. Experiments on 14 manipulation tasks across MetaWorld, ManiSkill, and Franka Kitchen show that STDR consistently improves sample efficiency and success rates over multiple baselines, and matches or surpasses handcrafted dense rewards on several challenging tasks. Real-robot evaluations further indicate that STDR assigns stable, progress-aligned rewards on successful executions while producing appropriately low rewards for failures, suggesting robustness to visual noise and better-calibrated reward assignment across settings.

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.

Reinforcement learning for robot manipulation is often bottlenecked by reward design, especially in long-horizon tasks: sparse success rewards provide weak supervision, while hand-crafted dense rewards are tedious to design and generalize poorly across tasks. Progress-based reward models offer a promising alternative by estimating how far an observation has advanced toward task completion, but existing approaches often require task-specific demonstrations or progress labels, and can assign high rewards to visually plausible but physically incorrect states. We introduce the Reference-Anchored Reward Model (RARM), a lightweight visual comparator that converts a single successful demonstration into a dense, progress-aware reward. RARM is trained once on general-purpose videos with a contrastive temporal objective, requiring no robot-specific data, task-specific reward labels, or per-task reward engineering. At deployment, RARM matches rollout clips to reference clips and rewards only confident forward progress, suppressing uncertain matches that may otherwise produce false-positive rewards. Across 9 simulated manipulation tasks from LIBERO and MetaWorld and 4 real-world tasks, RARM achieves the best overall success rates in subsequent RL training, with particularly large gains on long-horizon tasks such as cloth folding, where unreliable progress estimates are especially harmful.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for eliciting long-chain reasoning in large language models. However, existing methods based on Group Relative Policy Optimization (GRPO) rely on a binary outcome reward, which induces two structural failure modes: Zero-Advantage Collapse, in which all rollouts in a group share the same outcome and the gradient vanishes, and Hallucinated Certainty, in which the model becomes increasingly confident on incorrect rollouts late in training. We address both modes by densifying the reward with intrinsic signals computed entirely from the policy's own conditional probabilities, and propose ISPO (Intrinsic Signal Policy Optimization, which combines a sequence-level signal measuring how informative the thinking trajectory is for the final answer, with a token-level directional reward whose hallucinated-certainty hinge penalizes confidently-wrong predictions at critical decision tokens. Across three base models and five mathematical reasoning benchmarks, ISPO consistently outperforms competitive baselines, with the largest gains on the hardest benchmarks where zero-advantage collapse is most frequent, and training-dynamics diagnostics confirm that both failure modes are decreased.

Large language models show strong potential for automated code generation, but lack guarantees for correctness, quality, safety, and domain-specific constraints. For instance in robotics, where code generation is increasingly being used for planning and executing actions, awareness of the environment and physical constraints is critical. To facilitate the adaption of code-generating LLMs to diverse requirements, including domain-specific ones, we present a reinforcement learning framework that fine-tunes pre-trained LLMs using proximal policy optimization. Our customizable execution-aware reward formula captures and optimizes syntax, functional correctness, code style, security, and simulator executability. A token-level reward mapping mechanism enables effective credit assignment from execution outcomes to generated tokens. The framework is evaluated on general-purpose code generation (MBPP/MBPP+) and robotic program synthesis (RoboEval). The results show substantial improvements in functional correctness and simulator executability, including an absolute pass@1 increase of 19% on MBPP and a reduction in execution failures by 51% on RoboEval. These findings demonstrate that structured reinforcement learning can effectively align language models to correct program generation and domain-specific requirements.

Existing robotic foundation policies are trained primarily via large-scale imitation learning. While such models demonstrate strong capabilities, they often struggle with long-horizon tasks due to distribution shift and error accumulation. While reinforcement learning (RL) can finetune these models, it cannot work well across diverse tasks without manual reward engineering. We propose VLLR, a dense reward framework combining (1) an extrinsic reward from Large Language Models (LLMs) and Vision-Language Models (VLMs) for task progress recognition, and (2) an intrinsic reward based on policy self-certainty. VLLR uses LLMs to decompose tasks into verifiable subtasks and then VLMs to estimate progress to initialize the value function for a brief warm-up phase, avoiding prohibitive inference cost during full training; and self-certainty provides per-step intrinsic guidance throughout PPO finetuning. Ablation studies reveal complementary benefits: VLM-based value initialization primarily improves task completion efficiency, while self-certainty primarily enhances success rates, particularly on out-of-distribution tasks. On the CHORES benchmark covering mobile manipulation and navigation, VLLR achieves up to 56% absolute success rate gains over the pretrained policy, up to 5% gains over state-of-the-art RL finetuning methods on in-distribution tasks, and up to $10\%$ gains on out-of-distribution tasks, all without manual reward engineering. Additional visualizations can be found in https://silongyong.github.io/vllr_project_page/

Multimodal large language models (MLLMs) have achieved remarkable progress in vision-language tasks, but continue to struggle with spatial reasoning. Existing spatial MLLMs rely on large-scale datasets, explicit 3D inputs, architecture-specific modifications, or sparse Reinforcement Learning (RL) methods that provide insufficient guidance for spatially-grounded reasoning. We introduce SpatialThinker. To our knowledge, it is the first MLLM unifying Scene Graph Generation (SGG) and visual reasoning in a single pass via online RL. The model simulates human-like spatial perception by constructing a mental scene graph of task-relevant objects and relations, and reasoning toward an answer via dense spatial rewards. Our contributions are threefold: (1) SGG-grounded reasoning: integrating SGG directly within the reasoning chain rather than as a disjoint preprocessing step; (2) STVQA-7K: a high-quality spatial VQA training dataset via a scalable synthesis pipeline; and (3) a dense spatial reward design that enforces structured grounding during RL and generalizes to improve broad visual perception. SpatialThinker-7B achieves 3.6$\times$ larger gains over SFT and $1.7\times$ better in- and out-of-distribution generalization than sparse RL. Trained on only 7K samples, SpatialThinker-7B matches GPT-5 and outperforms GPT-4o, while SpatialThinker-30B surpasses both GPT-5 and Claude 4 Sonnet on average across 14 spatial and real-world benchmarks, demonstrating that structured spatial grounding with reward-aligned reasoning enables robust spatial understanding with limited data.