Robustness to Modeling Errors in Risk-Sensitive Markov Decision Problems with Markov Risk Measures

Abstract

We consider risk-sensitive Markov decision processes (MDPs), where the MDP model is influenced by a parameter which takes values in a compact metric space. We identify sufficient conditions under which small perturbations in the model parameters lead to small changes in the optimal value function and optimal policy. We further establish the robustness of the risk-sensitive optimal policies to modeling errors. Implications of the results for data-driven decision-making, decision-making with preference uncertainty, and systems with changing noise distributions are discussed.

24 pages, submitted to SIAM Journal on Control and Optimization