Model-free \(\mu\) Synthesis Via Adversarial Reinforcement Learning

Abstract

Motivated by the recent empirical success of policy-based reinforcement learning (RL), there has been a research trend studying the performance of policy-based RL methods on standard control benchmark problems. In this paper, we examine the effectiveness of policy-based RL methods on an important robust control problem, namely \(\mu\) synthesis. We build a connection between robust adversarial RL and \(\mu\) synthesis, and develop a model-free version of the well-known \(DK\)-iteration for solving state-feedback \(\mu\) synthesis with static \(D\)-scaling. In the proposed algorithm, the \(K\) step mimics the classical central path algorithm via incorporating a recently-developed double-loop adversarial RL method as a subroutine, and the \(D\) step is based on model-free finite difference approximation. Extensive numerical study is also presented to demonstrate the utility of our proposed model-free algorithm. Our study sheds new light on the connections between adversarial RL and robus

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