  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.
