Marginal Coverage Credit Reduces Redundant Exploration in Parallel State-Entropy Optimization

Policy Gradient for Parallel State Entropy maximization (PGPSE) expands state-space coverage by training independently parameterized policies in replicated copies of the same environment. However, its pooled team-entropy score measures only collective exploration and cannot identify policies that contribute non-redundant coverage. We introduce Marginal Coverage Credit for PGPSE (MCC-PGPSE), which combines leave-one-policy-out coverage with state-owner specialization to estimate policy-specific credit. MCC-PGPSE preserves PGPSE's pooled objective and redistributes non-negative auxiliary intrinsic rewards according to these credits without changing their total mass. This redistribution is designed to discourage redundant visitation and promote complementary coverage. We evaluated MCC-PGPSE in controlled environments, seven public discrete-state benchmarks, and representative Room and Maze settings from the original PGPSE protocol. Across all tested settings, MCC-PGPSE produced positive final window gains in normalized team state entropy and state support over the Entropy baseline. Controlled-task comparisons and the fixed-suite public aggregate were significant, whereas five-seed original-protocol comparisons were directionally consistent. Ablations and credit alignment controls indicate that most gains arise from leave-one-policy-out coverage rather than non-uniform weighting, mismatched credit, or neural novelty alone. These results support contribution-conditioned auxiliary reward allocation as an interpretable approach to improving complementary coverage among parallel policies in discrete state spaces.

Integrating Novelty and Surprise for Experience Prioritization and Exploration in Image-Based Reinforcement Learning

Sample efficiency is a central challenge in reinforcement learning (RL), particularly in image-based domains where agents must learn from high-dimensional visual inputs. Traditional sampling often relies on random or suboptimal experience selection, leading to redundant updates and slow learning. Improving efficiency requires mechanisms that prioritize informative experiences while also encouraging effective exploration. Prioritized Experience Replay (PER) addresses part of this challenge by reusing high-value transitions, while intrinsic rewards promote the exploration of novel or uncertain states. However, their integration has not been extensively studied. This paper introduces Novelty and Surprise Prioritized Experience Replay (NSPER), which uses novelty to capture underrepresented states and surprise to expose gaps in the agent's understanding of the environment. We further extend this with NSPER+R, integrating these signals as intrinsic rewards to jointly improve replay quality and exploration. Experiments on DeepMind Control Suite tasks show that NSPER and NSPER+R improve training efficiency and convergence speed compared to existing methods in image-based RL.

Explore Beyond the Boundary Using Entropic Information

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

Search-G1: Grounded Search Agents via Representation-Based Intrinsic Rewards

Search-augmented language agents should retrieve external information only when necessary and ground their answers in retrieved evidence. Existing external rewards provide either sparse outcome supervision or richer feedback from process annotations and LLM judges. Outcome rewards scale readily but cannot distinguish grounded retrieval from redundant search, whereas richer signals require costly annotation or inference during training. Internal rewards based on policy-side signals such as entropy, likelihood, or information gain are graded and inexpensive to evaluate, yet mainly reflect model confidence rather than evidence grounding. We propose Search-G1, a representation-based intrinsic reward framework that measures the operational grounding of an agent's answers through two intervention-calibrated readouts. A prompt-state readout predicts closed-book sufficiency, whose complement defines policy-relative retrieval necessity; an answer-commit readout estimates evidence reliance from answer-stage sensitivity to evidence deletion. Together, they provide additional credit to correct searched trajectories when retrieval is estimated necessary and the answer is evidence-sensitive, favor correct direct answers when closed-book knowledge suffices, and penalize repeated search. After calibration, reward scoring requires neither process annotations nor LLM-as-judge inference during policy optimization. Because reinforcement learning changes policy representations, Search-G1 periodically refits both readouts on trajectories from the latest checkpoint, allowing the reward to co-evolve with the policy. Experiments across multiple search-based question-answering benchmarks and two model scales show that Search-G1 improves the grounding--search-cost trade-off, producing shorter response-side trajectories at competitive task accuracy. Code is available at https://github.com/Rosy0912/Search-G1.

Reward-free Pretraining for Reinforcement Learning via Occupancy Coverage Maximization

Sparse rewards pose a central challenge in reinforcement learning, since agents receive no informative signal until they reach their goal. Intrinsic-reward methods address this issue by optimizing non-stationary objectives such as novelty, prediction error, or skill diversity, thereby injecting a supervision signal into the problem. While effective, these methods often require that the extrinsic (sparse) reward can be evaluated -- either online or during offline relabeling of the stored transitions. This limitation is particularly vexing for multi-task, meta-, and continual reinforcement learning, where agents' interactions with the environment are usually reward-free. In this work, we present a method to pre-train transferable exploration policies that rapidly adapt to sparse rewards at downstream task time. Our objective maximizes state-space covering for the occupancy measure, and can be framed in terms of entropy maximization. Its algorithmic implementation, ROVER, leverages recent advances on the operatorial formulation of RL to estimate occupancy with a learned resolvent world model, bypassing common hurdles associated with density and entropy estimation. ROVER further introduces a virtual "sink" state for unexplored regions, balancing coverage of known states with expansion into unseen ones and preventing cyclic expansion-collapse behavior during learning. In tabular and pixel-based sparse navigation tasks, ROVER produces more uniform aggregate coverage and stronger initializations for downstream tasks than standard reward-free baselines.

When Do Intrinsic Rewards Work for Code Reasoning? A Comprehensive Study

Reinforcement learning with verifiable rewards (RLVR) has driven substantial progress in large language model reasoning, but relies on ground-truth supervision that is costly or infeasible, especially in coding tasks. Recent work addresses this by deriving rewards from a model's own signals, such as majority voting or confidence-based scores, achieving notable success on mathematical reasoning benchmarks. However, code generation poses distinct challenges: programs are structurally complex, semantically equivalent solutions may differ syntactically, and verification typically requires execution. Whether these intrinsic reward methods transfer effectively to code remains unexplored. In this work, we present a systematic empirical study of intrinsic reward methods for code generation. We conduct extensive experiments on LiveCodeBench, systematically evaluating representative certainty-based Reinforcement Learning from Internal Feedback (RLIF) approaches under different training scenarios and hyperparameter settings. Our experiments reveal that certainty-based methods yield early gains but inevitably collapse: models progressively shorten outputs and lose reasoning capability, with collapse speed sensitive to sample size and temperature. When used to initialize RLVR training, RLIF pre-training offers no significant improvement over training from scratch. We also provide actionable recommendations for using intrinsic rewards for training code reasoning models. Our study shows both the promise and limitations of intrinsic reward methods for code, informing future work on code models and agents.

CIG: Exploration via Conditional Information Gain

Intrinsic rewards for exploration in reinforcement learning condition on different contexts: lifelong rewards score each transition against accumulated experience but ignore within-rollout redundancy; episodic rewards penalize intra-trajectory repetition but discard lifetime progress. Hybrid methods combine both signals through heuristic weights or require Gaussian-process dynamics that do not scale beyond low-dimensional state spaces. Trajectory-level information gain decomposes into per-step terms that condition on the replay buffer and rollout prefix simultaneously, but remains intractable for deep models. We derive the Conditional Information Gain (CIG) reward as a tractable surrogate: a log-determinant objective over an ensemble disagreement kernel whose Cholesky factorization yields causal per-step rewards that retain both conditioning sets while scaling to high-dimensional state spaces. We instantiate CIG in a model-based setting, where rollouts are short and within-rollout corrections remain largely unexplored. Across twelve tasks spanning discrete (MiniGrid) and continuous control (OGBench), in both clean and stochastic-distractor settings, CIG outperforms or matches prior exploration methods while remaining robust to stochastic distractors.