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We study finite episodic Markov decision processes incorporating dynamic riskmeasures to capture risk sensitivity. To this end, we present two model-basedalgorithms applied to \emph{Lipschitz} dynamic risk measures, a wide range ofrisk measures that subsumes spectral risk measure, optimized certaintyequivalent, distortion risk measures among others. We establish both regretupper bounds and lower bounds. Notably, our upper bounds demonstrate optimaldependencies on the number of actions and episodes, while reflecting theinherent trade-off between risk sensitivity and sample complexity.Additionally, we substantiate our theoretical results through numericalexperiments.

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