arXiv:2605.10909cs.LGstat.ML2026-05

提出新型多步策略梯度,可突破受限策略下的局部最优陷阱。

Revisiting Policy Gradients for Restricted Policy Classes: Escaping Myopic Local Optima with $k$-step Policy Gradients

论文配图:Revisiting Policy Gradients for Restricted Policy Classes: Escaping Myopic Local Optima with $k$-step Policy Gradients
图 1 · 摘自论文原文
  • 用k步Q函数替代单步,增强策略更新的长远视野。
  • 理论证明性能逼近最优确定性策略,误差随k指数下降。
  • 适合状态聚合、部分可观测多智能体等难解场景。

本文重新审视受限策略类上常用的策略梯度方法,发现其易陷入次优临界点,根源在于梯度本身具有短视性——仅基于单步Q函数优化。为此,提出广义k步策略梯度方法,通过耦合k步时间窗内的随机性,可逃离受限策略类中的短视局部最优。理论上证明该方法收敛至与最优确定性策略性能相差指数级的解(关于k)。进一步表明,结合投影梯度下降与镜像下降的k步策略梯度,在仅假设价值函数光滑可导的前提下,可在O(1/T)次迭代内达到此指数级保证。该方法避免了常见分布偏移项||d_μ^{π^*} / d_μ^π||_∞和||d_μ^{π^*} / μ||_∞,从而在完全可观测环境中也能摆脱由探索不足引发的次优临界点,为状态聚合及部分可观测协作多智能体等难题提供近优解。

原文摘要 · Abstract (English)

This work revisits standard policy gradient methods used on restricted policy classes, which are known to get stuck in suboptimal critical points. We identify an important cause for this phenomenon to be that the policy gradient is itself fundamentally myopic, i.e. it only improves the policy based on the one-step $Q$-function. In this work, we propose a generalized $k$-step policy gradient method that couples the randomness within a $k$-step time window and can escape the myopic local optima in MDPs with restricted policy classes. We show this new method is theoretically guaranteed to converge to a solution that is exponentially close in performance to the optimal deterministic policy with respect to $k$. Further, we show projected gradient descent and mirror descent with this $k$-step policy gradient can achieve this exponential guarantee in $O(\frac{1}{T})$ iterations, despite only assuming smoothness and differentiability of the value function. This will provide near optimal solutions to previously elusive applications like state aggregation and partially observable cooperative multi-agent settings. Moreover, our bounds avoid the ubiquitous distribution mismatch factors $||d_μ^{π^*} / d_μ^π||_\infty$ and $||d_μ^{π^*} / μ||_\infty$ enabling the $k$-step policy gradient method to escape suboptimal critical points that emerge from poor exploration in fully observable settings.

强化学习策略梯度多步优化局部最优

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