arXiv:2509.20509cs.LGcs.AI2025-09

用动态复杂度项替代熵正则化,让强化学习更稳定、少调参。

Complexity-Regularized Proximal Policy Optimization

  • 用熵与非均衡性的乘积定义自调节复杂度项
  • 在不同超参下表现稳定,无需精细调参
  • 适合对超参敏感的强化学习场景

策略梯度方法通常依赖熵正则化防止过早收敛,但盲目最大化熵会将策略推向均匀分布,若未调优,可能覆盖奖励信号。本文提出用自调节复杂度项替代标准熵项,该量为香农熵与非均衡性(衡量分布偏离均匀程度)的乘积。与纯熵不同,该复杂度在确定性和完全均匀分布时为零,仅在有序与随机共存时为正,能保留有益随机性,并在策略不确定时降低正则化压力,使学习聚焦于奖励优化。我们提出复杂度正则化近端策略优化(CR-PPO),实验证明其对超参数选择显著更鲁棒,在多个数量级的正则化系数下表现一致,且在无需正则化时无害,大幅减少昂贵的超参数调优需求。

原文摘要 · Abstract (English)

Policy gradient methods usually rely on entropy regularization to prevent premature convergence. However, maximizing entropy indiscriminately pushes the policy towards a uniform distribution, often overriding the reward signal if not optimally tuned. We propose replacing the standard entropy term with a self-regulating complexity term, defined as the product of Shannon entropy and disequilibrium, where the latter quantifies the distance from the uniform distribution. Unlike pure entropy, which favors maximal disorder, this complexity measure is zero for both fully deterministic and perfectly uniform distributions, i.e., it is strictly positive for systems that exhibit a meaningful interplay between order and randomness. These properties ensure the policy maintains beneficial stochasticity while reducing regularization pressure when the policy is highly uncertain, allowing learning to focus on reward optimization. We introduce Complexity-Regularized Proximal Policy Optimization (CR-PPO), a modification of PPO that leverages this dynamic. We empirically demonstrate that CR-PPO is significantly more robust to hyperparameter selection than entropy-regularized PPO, achieving consistent performance across orders of magnitude of regularization coefficients and remaining harmless when regularization is unnecessary, thereby reducing the need for expensive hyperparameter tuning.

强化学习PPO正则化超参鲁棒

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