Myopic Bounds for Optimal Policy of POMDPs: An Extension of Lovejoy’s Structural Results

This paper provides a relaxation of the sufficient conditions and an extension of the structural results for partially observed Markov decision processes (POMDPs) obtained by Lovejoy in 1987. Sufficient conditions are provided so that the optimal policy can be upper and lower bounded by judiciously chosen myopic policies. These myopic policy bounds are constructed to maximize the volume of belief states where they coincide with the optimal policy. Numerical examples illustrate these myopic bounds for both continuous and discrete observation sets.