Regret Bounds for Risk-sensitive Reinforcement Learning with Lipschitz Dynamic Risk Measures
Machine Learning
2023-06-06 v1 Artificial Intelligence
Machine Learning
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.
Cite
@article{arxiv.2306.02399,
title = {Regret Bounds for Risk-sensitive Reinforcement Learning with Lipschitz Dynamic Risk Measures},
author = {Hao Liang and Zhi-quan Luo},
journal= {arXiv preprint arXiv:2306.02399},
year = {2023}
}