Abstract

We seek to find the robust policy that maximizes the expected cumulative reward for the worst case when a partially observable Markov decision process (POMDP) has uncertain parameters whose values are only known to be in a given region. We prove that the robust value function, which represents the expected cumulative reward that can be obtained with the robust policy, is convex with respect to the belief state. Based on the convexity, we design a value-iteration algorithm for finding the robust policy. We prove that our value iteration converges for an infinite horizon. We also design point-based value iteration for fining the robust policy more efficiency possibly with approximation. Numerical experiments show that our point-based value iteration can adequately find robust policies.