提出一种新方法,让智能体在受限条件下高效探索并保证结果最优可行。
Global Optimality for Constrained Exploration via Penalty Regularization

- 用二次惩罚项将约束转化为伪奖励,直接优化策略空间
- 在非凸情况下仍能收敛到近似最优且满足约束的策略
- 适合需要安全或资源限制的强化学习任务
高效探索是强化学习的核心问题,常被形式化为最大化状态-动作占用分布的熵。然而,现实中的探索常受安全、资源或模仿等约束,这类受限场景极具挑战:熵最大化缺乏可加结构,导致基于贝尔曼方程的方法失效;同时,策略参数化引入目标与约束的非凸性。现有模型无关的策略梯度方法仅提供弱遗憾和遍历平均的保证,无法确保最终输出是一个近优且几乎可行的单一部署策略。本文提出单循环的策略梯度惩罚(PGP)方法,通过二次惩罚正则化实现一般凸占用测量约束。PGP构造伪奖励以获得惩罚目标的梯度估计,并利用经典策略梯度定理。我们证明了惩罚目标的正则性,提供了收敛所需的光滑性。借助隐藏凸性和强对偶性,建立全局末次迭代收敛性,即使在策略诱导非凸下,仍可达到ε-最优约束熵值且约束违反不超过ε。我们在网格世界基准上进行消融实验,并在两个复杂的连续控制任务中验证其可扩展性。
原文摘要 · Abstract (English)
Efficient exploration is a central problem in reinforcement learning and is often formalized as maximizing the entropy of the state-action occupancy measure. While unconstrained maximum-entropy exploration is relatively well understood, real-world exploration is often constrained by safety, resource, or imitation requirements. This constrained setting is particularly challenging because entropy maximization lacks additive structure, rendering Bellman-equation-based methods inapplicable. Moreover, scalable approaches require policy parameterization, inducing non-convexity in both the objective and the constraints. To our knowledge, the only prior model-free policy-gradient approach for this setting under general policy parameterization is due to Ying et al. (2025). Unfortunately, their guarantees are limited to weak regret and ergodic averages, which do not imply that the final output is a single deployable policy that is near-optimal and nearly feasible. In this work we take a different approach to this problem, and propose Policy Gradient Penalty (PGP) method, a single-loop policy-space method that enforces general convex occupancy-measure constraints via quadratic-penalty regularization. PGP constructs pseudo-rewards that yield gradient estimates of the penalized objective, subsequently exploiting the classical Policy Gradient Theorem. We further establish the regularity of the penalized objective, providing the smoothness properties needed to justify the convergence of PGP. Leveraging hidden convexity and strong duality, we then establish global last-iterate convergence guarantees, attaining an $ε$-optimal constrained entropy value with $ε$ bounded constraint violation despite policy-induced non-convexity. We validate PGP through ablations on a grid-world benchmark and further demonstrate scalability on two challenging continuous-control tasks.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。