Solving Structured Continuous-Time Markov Decision Processes

Abstract

We present an approach to solving structured continuous-time Markov decision processes. We approximate the the optimal value function by a compact linear form, resulting in a linear program. The main difculty arises from the number of constraints that grow exponentially with the number of variables in the system. We exploit the representation of continuous-time Bayesian networks (CTBNs) to describe the Markov process. We show that by exploiting the structure of the CTBN, we can reduce the growth in the number of constraints to be polynomial. We provide theoretic bounds on the quality of the approximation and experimental results on problems of different sizes, demonstrating the scalability and delity of our approach.