Regret Bounds for Risk-sensitive Reinforcement Learning with Lipschitz Dynamic Risk Measures
This work addresses risk sensitivity in decision-making for reinforcement learning applications, representing an incremental advance with specific theoretical contributions.
The authors tackled the problem of risk-sensitive reinforcement learning by introducing model-based algorithms for Lipschitz dynamic risk measures, establishing optimal regret bounds that show a trade-off between risk sensitivity and sample complexity, with theoretical results validated through numerical experiments.
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.