Sequential Decision-Making under Uncertainty: A Robust MDPs review

Abstract: Fueled by both advances in robust optimization theory and applications of reinforcement learning, robust Markov Decision Processes (RMDPs) have gained increasing attention, due to their powerful capability for sequential decision-making under uncertainty. This review provides an in-depth overview of the evolution and advances in RMDPs formulations, particularly in ambiguity modeling, and classifies these methods for representing uncertainty into three principal approaches: parametric, moment-based, and discrepancy-based, elaborating the trade-offs among the alternative representations. Meanwhile, the review delves into the rectangular assumptions, which guarantee the tractability of RMDPs yet are noted for their conservatism. The review summarizes three popular rectangular conditions and develops a new proof to attest to the NP-hardness of non-rectangular RMDPs. Out of the traditional RMDPs scope, recent efforts without conventional rectangular assumptions and new fashions within the RMDPs community are also reviewed. These studies foster the development of more flexible and practical modeling frameworks and enhance the adaptability and performance of RMDPs.