Computationally Feasible Bounds for Partially Observed Markov Decision Processes

A partially observed Markov decision process (POMDP) is a sequential decision problem where information concerning parameters of interest is incomplete, and possible actions include sampling, surveying, or otherwise collecting additional information. Such problems can theoretically be solved as dynamic programs, but the relevant state space is infinite, which inhibits algorithmic solution. This paper explains how to approximate the state space by a finite grid of points, and use that grid to construct upper and lower value function bounds, generate approximate nonstationary and stationary policies, and bound the value loss relative to optimal for using these policies in the decision problem. A numerical example illustrates the methodology.