Entropy control has become an effective tool in reinforcement learning (RL) of large language models (LLMs), helping balance exploration-exploitation trade-off during alignment process. Such RL paradigm is often conducted on mixtures of heterogeneous tasks, which induce distinct entropy regimes under the same policy, making global or token-level entropy regulation insufficient to corresponding heterogeneous needs of exploration. This heterogeneity further makes GRPO-style normalized advantages induce an entropy-dependent bias, making advantage signals across prompt groups statistically non-comparable. To address this issue, we propose Group Entropy-Controlled Policy Optimization (GEPO), a lightweight extension to GRPO that uses group entropy, estimated from existing grouped samples to perform entropy-conditioned asymmetric advantage shaping. GEPO attenuates positive advantages in low-entropy groups to reduce over-exploitation, and negative advantages in high-entropy groups to preserve exploration, with adaptive thresholds derived from historical entropy statistics. Extensive experiments on two base models across thirteen benchmarks spanning mathematics, physics, science, code generation, and instruction following show that GEPO consistently outperforms GRPO and recent entropy-controlled methods, delivering balanced cross-task improvements while preserving task-specific exploration levels throughout training.
Recent breakthroughs of Reinforcement Learning (RL) have highlighted its potential for complex agentic Large Language Model (LLM) tasks. However, existing efforts largely focus on single-task settings, whereas real-world deployment necessitates a generalist agent capable of solving multiple tasks simultaneously. In this work, we identify a critical yet underexplored phenomenon in multi-task agentic RL: different tasks can exhibit exploration-exploitation pace mismatch. Specifically, easier tasks may converge early to low-entropy policies that hinder learning on harder tasks, while harder tasks can, in turn, push easier tasks back toward high-entropy exploration. This back-and-forth interaction creates inter-task entropy crossovers and frequent entropy spikes. Inspired by this observation, we introduce Entropy Pacing Policy Optimization (EPPO) for multi-task agentic LLMs, which coordinates entropy across tasks to stabilize multi-task optimization. At the core of EPPO is a task-wise dynamic clipping mechanism that replaces the fixed clipping threshold in Group Relative Policy Optimization (GRPO) with a task entropy-aware adaptive bound, tightening updates for over-confident tasks while relaxing them for under-explored ones. Experiments on the multi-task agentic benchmarks demonstrate that the proposed EPPO yields results superior to its counterparts.
Reinforcement Learning with Verifiable Rewards (RLVR) has significantly advanced Large Language Model (LLM) reasoning; however, it faces a fundamental optimization instability: uniform token updates precipitate entropy collapse, leading to premature convergence to suboptimal strategies, whereas excessive Shannon Entropy maximization can cause entropy explosion, driving blind exploration toward incoherent reasoning chains. To resolve this dichotomy, we introduce the Independent Combinatorial Tokens (ICT) framework, which shifts the optimization focus from scalar uncertainty to the distributional properties of token logits. By leveraging the Jensen-Shannon (JS) divergence between token logits distributions, ICT identifies tokens with distinctive distributional patterns as critical branching points for guiding effective exploration in LLM reasoning. Our theoretical analysis, grounded in both Shannon and second-order Rényi entropy, proves that selectively updating on these tokens regulates policy concentration: it reduces the overall distribution uncertainty measured by Shannon entropy, while controlling probability concentration captured by second-order Rényi entropy. This dual effect prevents over-concentrated token generation from weakening exploration and effectively stabilizes the training landscape. Empirical results demonstrate that updating only the top 10% of unique tokens on Qwen2.5 (0.5B/1.5B/7B) models yields an average pass@4 improvement of 4.58%, with a maximum gain of 14.9%, over GRPO, 20-Entropy, and STAPO baselines across seven benchmarks spanning math, commonsense, and Olympiad-level problems.
Bolian Li, Yifan Wang, Yi Ding +3cs.LG cs.CL stat.ML
Reinforcement learning (RL) has unlocked complex reasoning abilities in large language models (LLMs). However, most RL algorithms suffer from performance saturation, preventing further gains as RL training scales. This problem can be characterized by the collapse of entropy, a key diagnostic for exploration in RL. Existing attempts have tried to prevent entropy collapse through regularization or clipping, but their resulting entropy curves often exhibit instability in the long term, which hinders performance gains. In this paper, we introduce Entrocraft, a simple rejection-sampling approach that realizes any user-customized entropy schedule by biasing the advantage distributions. Entrocraft requires no objective regularization and is advantage-estimator-agnostic. Theoretically, we relate per-step entropy change to the advantage distribution under minimal assumptions, which explains the behavior of existing RL and entropy-preserving methods. Entrocraft also enables a systematic study of entropy schedules, where we find that linear annealing, which starts high and decays to a slightly lower target, performs best. Empirically, Entrocraft addresses performance saturation, significantly improving generalization, output diversity, and long-term training. It enables a 4B model to outperform an 8B baseline, sustains improvement for up to 4x longer before plateauing, and raises pass@K by 50% over the baseline.