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Direct policy search serves as one of the workhorses in modern reinforcementlearning (RL), and its applications in continuous control tasks have recentlyattracted increasing attention. In this work, we investigate the convergencetheory of policy gradient (PG) methods for learning the linear risk-sensitiveand robust controller. In particular, we develop PG methods that can beimplemented in a derivative-free fashion by sampling system trajectories, andestablish both global convergence and sample complexity results in thesolutions of two fundamental settings in risk-sensitive and robust control: thefinite-horizon linear exponential quadratic Gaussian, and the finite-horizonlinear-quadratic disturbance attenuation problems. As a by-product, our resultsalso provide the first sample complexity for the global convergence of PGmethods on solving zero-sum linear-quadratic dynamic games, anonconvex-nonconcave minimax optimization problem that serves as a baselinesetting in multi-agent reinforcement learning (MARL) with continuous spaces.One feature of our algorithms is that during the learning phase, a certainlevel of robustness/risk-sensitivity of the controller is preserved, which wetermed as the implicit regularization property, and is an essential requirementin safety-critical control systems.

Derivative-Free Policy Optimization for Linear Risk-Sensitive and Robust Control Design: Implicit Regularization and Sample Complexity