Poster
Regret Bounds for Episodic Risk-Sensitive Linear Quadratic Regulator
Wenhao Xu · Xuefeng Gao · Xuedong He
Hall 3 + Hall 2B #416
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Abstract
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Sat 26 Apr midnight PDT
— 2:30 a.m. PDT
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 ˜O(logN) 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 ˜O(√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.
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