Algorithmic Optimality Guarantees for Nonsmooth $H_\infty$ Output-Feedback Policy Search

2026-09-05

AI Summary

研究了非凸且非光滑的连续时间全阶动态输出反馈H∞策略搜索问题，通过扩展凸提升方法证明了ε-平稳性与O(ε)次优性的关系，并提出了一种非严格可行性二分法以获得ε最优稳定控制器。

Abstract

We study continuous-time full-order dynamic output-feedback $H_\infty$ policy search, a nonconvex and nonsmooth problem. Direct policy search is a central paradigm in reinforcement learning and continuous control, but rigorous guarantees remain scarce in robust output-feedback settings. The $H_\infty$ problem is a canonical benchmark because it captures disturbance attenuation and robustness while exposing the hard nonsmooth geometry of policy-space optimization. We prove that on the exact identity-gauge slice of the extended convex lift, $\varepsilon$-stationarity yields $O(\varepsilon)$-suboptimality on compact exact slices, which in turn yields convergence-rate guarantees for nonsmooth policy-search methods. This result addresses the finite-time optimality-gap question raised by Guo and Hu [2022] in the more general dynamic output-feedback $H_\infty$ policy-search setting. We further use the established value equivalence supplied by extended convex lifting to formulate a nonstrict-feasibility bisection method with one final strict-feasibility recovery step, yielding an explicit $\varepsilon$-optimal stabilizing controller. These results provide a quantitative and algorithmic strengthening of prior qualitative optimality theory for nonsmooth $H_\infty$ policy search.

Problem

• nonconvex
• nonsmooth
• H∞ control
• output-feedback
• policy search

Innovation

• nonsmooth H∞ policy search
• extended convex lifting
• ε-stationarity
• nonstrict-feasibility bisection method