Regret Bounds for Episodic Risk-Sensitive Linear Quadratic Regulator

Wenhao XU, Xuefeng Gao, Xuedong He

Keywords: reinforcement Learning, regret, LEQR, finite horizon, episodic setting

Abstract:

Risk-sensitive linear quadratic regulator is one of the most fundamental problems in risk-sensitive optimal control.
In this paper, we study online adaptive control of risk-sensitive linear quadratic regulator in the finite horizon episodic setting.
We propose a simple least-squares greedy algorithm and show that it achieves $\widetilde{\mathcal{O}}(\log N)$ regret under a specific identifiability assumption, where $N$ is the total number of episodes. If the identifiability assumption is not satisfied, we propose incorporating exploration noise into the least-squares-based algorithm, resulting in an algorithm with $\widetilde{\mathcal{O}}(\sqrt{N})$ regret.
To our best knowledge, this is the first set of regret bounds for episodic risk-sensitive linear quadratic regulator.
Our proof relies on perturbation analysis of less-standard Riccati equations for risk-sensitive linear quadratic control, and a delicate analysis of the loss in the risk-sensitive performance criterion due to applying the suboptimal controller in the online learning process.

Primary Area: learning theory

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Submission Number: 5359