Risk-averse formulations of Stochastic Optimal Control and Markov Decision Processes

Alexander Shapiro; Yan Li

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arXiv · 2505.16651

Risk-averse formulations of Stochastic Optimal Control and Markov Decision Processes

Alexander Shapiro·Yan Li

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Abstract

The aim of this paper is to investigate risk-averse and distributionally robust modeling of Stochastic Optimal Control (SOC) and Markov Decision Process (MDP). We discuss construction of conditional nested risk functionals, a particular attention is given to the Value-at-Risk measure. Necessary and sufficient conditions for existence of non-randomized optimal policies in the framework of robust SOC and MDP are derived. We also investigate sample complexity of optimization problems involving the Value-at-Risk measure.

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Alexander Shapiro, Yan Li. 2025-05-22. Risk-averse formulations of Stochastic Optimal Control and Markov Decision Processes. https://arxiv.org/abs/2505.16651

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