Algorithmic Optimality Guarantees for Nonsmooth H∞ Output-Feedback Policy Search
Abstract
We study continuous-time full-order dynamic output-feedback H∞ 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∞ 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, ε-stationarity yields O(ε)-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∞ 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 ε-optimal stabilizing controller. These results provide a quantitative and algorithmic strengthening of prior qualitative optimality theory for nonsmooth H∞ policy search.
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BibTeX
@misc{soleymani2026algorithmic,
title = {{Algorithmic Optimality Guarantees for Nonsmooth $H_\infty$ Output-Feedback Policy Search}},
author = {Ashkan Soleymani and Patrick Jaillet},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06197},
eprint = {2609.06197},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06197},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Algorithmic Optimality Guarantees for Nonsmooth H_∞ Output-Feedback Policy Search
AU - Ashkan Soleymani
AU - Patrick Jaillet
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.06197
UR - https://arxiv.org/abs/2609.06197
AB - We study continuous-time full-order dynamic output-feedback H_∞ 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_∞ 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, ε-stationarity yields O(ε)-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_∞ 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 ε-optimal stabilizing controller. These results provide a quantitative and algorithmic strengthening of prior qualitative optimality theory for nonsmooth H_∞ policy search.
ER -