Regret Bounds for Risk-sensitive Reinforcement Learning with Lipschitz Dynamic Risk Measures

• URL: http://arxiv.org/abs/2306.02399v1
• Date: Sun, 4 Jun 2023 16:24:19 GMT
• Title: Regret Bounds for Risk-sensitive Reinforcement Learning with Lipschitz Dynamic Risk Measures
• Authors: Hao Liang, Zhi-quan Luo
• Abstract summary: We present two model-based algorithms applied to emphLipschitz dynamic risk measures. Notably, our upper bounds demonstrate optimal dependencies on the number of actions and episodes.
• Score: 23.46659319363579
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study finite episodic Markov decision processes incorporating dynamic risk measures to capture risk sensitivity. To this end, we present two model-based algorithms applied to \emph{Lipschitz} dynamic risk measures, a wide range of risk measures that subsumes spectral risk measure, optimized certainty equivalent, distortion risk measures among others. We establish both regret upper bounds and lower bounds. Notably, our upper bounds demonstrate optimal dependencies on the number of actions and episodes, while reflecting the inherent trade-off between risk sensitivity and sample complexity. Additionally, we substantiate our theoretical results through numerical experiments.

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