Sleeping Experts and Bandits Approach to Constrained Markov Decision Processes

This brief paper presents simple simulation-based algorithms for obtaining an approximately optimal policy in a given finite set in large finite constrained Markov decision processes. The algorithms are adapted from playing strategies for “sleeping experts and bandits” problem and their computational complexities are independent of state and action space sizes if the given policy set is relatively small. We establish convergence of their expected performances to the value of an optimal policy and convergence rates, and also almost-sure convergence to an optimal policy with an exponential rate for the algorithm adapted within the context of sleeping experts.