# Policy Optimization in Robust Control: Weak Convexity and Subgradient Methods

arXiv: https://arxiv.org/abs/2509.25633 · HTML: https://mlsanity.com/paper/2509.25633/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2025.

## Built on by (most cited first, 2 of 2)

- [Gradient Dominance in the Linear Quadratic Regulator: A Unified Analysis for Continuous-Time and Discrete-Time Systems](https://mlsanity.com/paper/2602.22577/) (2026)
- [Algorithmic Optimality Guarantees for Nonsmooth H_∞ Output-Feedback Policy Search](https://mlsanity.com/paper/2609.06197/) (2026)

## Abstract (arXiv)

Robust control seeks stabilizing policies that perform reliably under adversarial disturbances, with H_∞ control as a classical formulation. It is known that policy optimization of robust H_∞ control naturally lead to nonsmooth and nonconvex problems. This paper builds on recent advances in nonsmooth optimization to analyze discrete-time static output-feedback H_∞ control. We show that the H_∞ cost is weakly convex over any convex subset of a sublevel set. This structural property allows us to establish the first non-asymptotic deterministic convergence rate for the subgradient method under suitable assumptions. In addition, we prove a weak Polyak-Lojasiewicz (PL) inequality in the state-feedback case, implying that all stationary points are globally optimal. We finally present a few numerical examples to validate the theoretical results.