2025/05/22 by Alexander Shapiro, Yan Li, Shapiro, Alexander +1
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #FOS: Mathematics #Optimization and Control (math.OC) #Reinforcement Learning in Robotics #Risk and Portfolio Optimization #Statistics Theory (math.ST) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2505.16651
openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.