Computer Science > Machine Learning
[Submitted on 30 Jan 2023 (v1), last revised 8 Jun 2023 (this version, v2)]
Title:Regret Bounds for Markov Decision Processes with Recursive Optimized Certainty Equivalents
View PDFAbstract:The optimized certainty equivalent (OCE) is a family of risk measures that cover important examples such as entropic risk, conditional value-at-risk and mean-variance models. In this paper, we propose a new episodic risk-sensitive reinforcement learning formulation based on tabular Markov decision processes with recursive OCEs. We design an efficient learning algorithm for this problem based on value iteration and upper confidence bound. We derive an upper bound on the regret of the proposed algorithm, and also establish a minimax lower bound. Our bounds show that the regret rate achieved by our proposed algorithm has optimal dependence on the number of episodes and the number of actions.
Submission history
From: Xuefeng Gao [view email][v1] Mon, 30 Jan 2023 01:22:31 UTC (224 KB)
[v2] Thu, 8 Jun 2023 07:47:46 UTC (224 KB)
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