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.

翻译：我们研究了有限回合马尔可夫决策过程，其中引入了动态风险度量以捕捉风险敏感性。为此，我们提出了两种基于模型的算法，应用于\emph{Lipschitz}动态风险度量，这是一类广泛的度量标准，包括谱风险度量、优化确定性等价、扭曲风险度量等。我们建立了遗憾上界和下界。值得注意的是，我们的上界在动作数量和回合数上表现出最优依赖关系，同时反映了风险敏感性与样本复杂性之间的内在权衡。此外，我们通过数值实验验证了理论结果。