arXiv:2608.10204cs.LG2026-08

让强化学习政策自动贴合安全边界,提升奖励同时更严格守规。

Boundary-Seeking Policy Gradient for Safe Reinforcement Learning

论文配图:Boundary-Seeking Policy Gradient for Safe Reinforcement Learning
图 1 · 摘自论文原文
  • 设计梯度更新方向,既优化奖励又主动靠近安全边界。
  • 在导航任务中比基线方法获得更高奖励且更紧贴安全边界。
  • 无需学习对偶变量,理论保证收敛到约束边界并满足最优条件。

安全强化学习在满足安全约束的前提下最大化奖励。对于约束马尔可夫决策过程,基于占据测度的线性规划视角表明:当约束在最优解处起作用时,最优策略恰好位于约束边界上。然而,标准梯度方法不利用此结构,常停留在可行域内部。本文提出边界追逐策略梯度(BSPG),一种一阶方法,其更新方向包含切向分量(在保持代价不变的前提下提升奖励)与法向分量(由残差驱动,从任意侧引导策略向激活边界移动)。组合方向具有代数拉格朗日形式,内含诱导系数而无需学习对偶变量。在精确梯度与设定正则条件下,约束残差以有限时域 $O(1/\ oot2\of{T})$ 收敛至零,切向分量为边界上的奖励上升方向,任何收敛参数序列在激活约束集上均为驻点,当极限也是可行集上的局部最大值时,满足KKT条件。这补足了现有分析——仅保证可行性,未刻画收敛时的约束取值。在标准Safety-Gymnasium导航任务中,BSPG实现更高奖励,并更紧密追踪边界,优于对比基线。

原文摘要 · Abstract (English)

Safe reinforcement learning maximizes reward subject to safety constraints. For Constrained Markov Decision Processes, the linear-programming view over occupancy measures implies that whenever the constraint is active at optimality, the optimal policy lies exactly on the constraint boundary, yet standard gradient-based methods do not exploit this structure and often settle in the feasible interior. We introduce Boundary-Seeking Policy Gradient (BSPG), a first-order method whose update combines a tangential component that improves reward while preserving cost to first order with a signed, residual-driven normal component that regulates the policy toward the active boundary from either side; the combined direction admits an algebraic Lagrangian form with an induced coefficient and no learned dual variable. Under exact gradients and stated regularity conditions, the constraint residual converges to zero from either side with a finite-horizon $O(1/\sqrt{T})$ bound, the tangential component is a reward-ascent direction on the boundary, and any convergent parameter sequence is stationary on the active constraint set, satisfying the KKT conditions when the limit is also a local maximizer over the feasible set. This complements existing analyses, which certify feasibility but do not characterize the constraint value at convergence. On a standard Safety-Gymnasium navigation task, BSPG attains higher reward while tracking the boundary more tightly than the compared baselines.

强化学习安全控制策略梯度约束优化

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