Sample Complexity for Markov Decision Processes and Stochastic Optimal Control with Static Risk Measures

Abstract

We present an elementary state augmentation method for a class of static risk measure applied to the total cost for both Markov decision processes (MDPs) and stochastic optimal control (SOC), such that dynamic programming equations can be derived on the augmented space. Through this we discuss the sample complexities of these two problem classes. We demonstrate the application of the proposed approach by developing a general framework for studying risk-averse MDPs and SOCs with distributionally robust functional generated by $\varphi$-divergences, and obtain new sample complexity results for commonly used divergence functions.