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In this paper we present a review of the connections between classicalalgorithms for solving Markov Decision Processes (MDPs) and classicalgradient-based algorithms in convex optimization. Some of these connectionsdate as far back as the 1980s, but they have gained momentum in recent yearsand have lead to faster algorithms for solving MDPs. In particular, two of themost popular methods for solving MDPs, Value Iteration and Policy Iteration,can be linked to first-order and second-order methods in convex optimization.In addition, recent results in quasi-Newton methods lead to novel algorithmsfor MDPs, such as Anderson acceleration. By explicitly classifying algorithmsfor MDPs as first-order, second-order, and quasi-Newton methods, we hope toprovide a better understanding of these algorithms, and, further expanding thisanalogy, to help to develop novel algorithms for MDPs, based on recent advancesin convex optimization.

From Convex Optimization to MDPs: A Review of First-Order, Second-Order and Quasi-Newton Methods for MDPs