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POMDP Structural Results for Controlled Sensing using Lehmann Precision

This paper provides sufficient conditions so that the optimal policy of a partially observed Markov decision process (POMDP) can be lower bounded by a myopic policy. The two new proposed conditions, namely, Lehmann precision and copositive dominance, completely fix the problems with two crucial assumptions in the well known papers Lovejoy (1987) and Rieder (1991). For controlled sensing POMDPs, Lehmann precision exploits both convexity and monotonicity of the value function, whereas the well known Blackwell dominance only exploits convexity. Numerical examples compare Lehmann precision with Blackwell dominance.