An MILP-Based Solution Scheme for Factored and Robust Factored Markov Decision Processes

Factored Markov decision processes (MDPs) are a prominent paradigm within the artificial intelligence community for modeling and solving large-scale MDPs whose rewards and dynamics decompose into smaller, loosely interacting components. Through the use of dynamic Bayesian networks and context-specific independence, factored MDPs can achieve an exponential reduction in the state space of an MDP and thus scale to problem sizes that are beyond the reach of classical MDP algorithms. However, factored MDPs are typically solved using custom-designed algorithms that can require meticulous implementations and considerable fine-tuning. In this paper, we propose a mathematical programming approach to solving factored MDPs. In contrast to existing solution schemes, our approach leverages off-the-shelf solvers, which allows for a streamlined implementation and maintenance; it effectively capitalizes on the factored structure present in both state and action spaces; and it readily extends to the largely unexplored class of robust factored MDPs, whose transition kernels are only known to reside in a pre-specified ambiguity set. Our numerical experiments demonstrate the potential of our approach.