Density-Aware Reward Scaling: A Reinforcement Learning Framework for Reward-Proportional Sampling

Multi-reward reinforcement learning trains large language models to satisfy multiple behavioral objectives simultaneously. Reward-wise normalization, as used in GDPO, preserves reward-specific relative information within rollout groups, but different objectives can still exhibit uneven learning progress. We study this behavior through advantage energy, the sum of a reward's squared advantages over a batch. Under idealized GDPO normalization, we show that this energy is proportional to active-group density: the fraction of rollout groups in which the reward provides nonzero relative advantages. This reveals a residual batch-level signal imbalance and provides a basis for calibrating reward contributions. Based on this relation, we propose Density-Aware Reward Aggregation (DARA). We derive an inverse-square-root density correction that gives greater weight to signals from less frequently active rewards. DARA computes its weights from each rollout batch, adapting to changes in reward activity throughout training without modifying the underlying policy optimization objective. Experiments on tool calling and mathematical reasoning show that DARA learns the targeted behaviors faster than GDPO, reaching high format compliance in up to 26% fewer training steps on tool calling and near-saturated length compliance in up to 65% fewer steps on mathematical reasoning, while remaining competitive in final performance. Our code is available at https://github.com/zhaihaotian/DARA.

While Reinforcement Learning (RL) enhances Large Language Model reasoning, on-policy algorithms like GRPO are sample-inefficient as they discard past rollouts. Existing experience replay methods address this by reusing accurate samples for direct policy updates, but this can incur additional storage costs and concentrate the policy on a narrow set of solutions. We argue that historical data should prioritize sustaining local policy plasticity rather than simply reinforcing accuracy. We define local policy plasticity as a persistent ability to remain backtrackable and switchable with respect to recent successful trajectories: throughout training, the policy maintains non-negligible support on recently reachable alternatives, so it can smoothly reallocate probability mass when needed without being locked into a single dominant path. To this end, we propose Dynamic Jensen-Shannon Replay (DyJR), a simple yet effective regularization framework using a dynamic reference distribution from recent trajectories. DyJR introduces two innovations: (1) A Time-Sensitive Dynamic Buffer that uses FIFO and adaptive sizing to retain only temporally proximal samples, synchronizing with model evolution; and (2) Jensen-Shannon Divergence Regularization, which replaces direct replay policy-gradient updates with a regularization signal that discourages premature over-commitment to a single Rank-1 trajectory. Experiments on mathematical reasoning, Text-to-SQL, and coding benchmarks demonstrate that DyJR improves over GRPO as well as baselines such as RLEP and Ex-GRPO, while maintaining training efficiency comparable to the original GRPO. Furthermore, Rank-k token probability evolution and semantic-mode analyses show reduced concentration and greater retention of alternative continuations. Matched admission-objective comparisons and repeated runs provide additional evidence for the roles of DyJR's components.

The goal of Quality-Diversity Reinforcement Learning (QD-RL) is to find a population of high-performing policies that solve a decision-making problem in diverse ways. Despite recent progress, QD-RL methods predominantly rely on evolutionary operators--including black-box optimizers, mutations, and crossovers--to facilitate exploration and induce diversity. Scaling these methods becomes increasingly costly as policies and behavior spaces grow larger. Building on the Soft QD view of quality-diversity optimization, we introduce Repulsive Population Policy Optimization (RePPO), which adapts PPO to jointly optimize a compact population of diverse, high-quality policies using a population-dependent, dynamically shaped reward. On standard continuous-control tasks, RePPO achieves a strong quality-diversity tradeoff compared with state-of-the-art QD-RL methods. Ablations further characterize this tradeoff by examining how each component affects individual quality and collective diversity. To assess RePPO's scalability, we extend our evaluation to learning from pixels and fine-tuning large language models. In pixel-based tasks, where large policies make most traditional QD-RL methods infeasible, RePPO maintains quality on par with standard PPO while achieving substantially higher diversity. Its successful application to language model fine-tuning further demonstrates, for the first time, that QD-RL methods can scale to this domain. Together, these results show that directly optimizing compact populations with RePPO provides a scalable approach to QD-RL across increasingly complex domains.