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Optimal policies for partially observed Markov decision processes (POMDPs)are history-dependent: Decisions are made based on the entire history ofobservation. Memoryless policies, which take decisions based on the lastobservation only, are generally considered useless in the literature because wecan construct POMDP instances for which optimal memoryless policies arearbitrarily worse than history-dependent ones. Our purpose is to challenge thisbelief. We show that optimal memoryless policies can be computed efficientlyusing mixed integer linear programming (MILP), and perform reasonably well on awide range of instances from the literature. When strengthened with validinequalities, the linear relaxation of this MILP provides high qualityupper-bounds on the value of an optimal history dependent policy. Furthermore,when used with a finite horizon POMDP problem with memoryless policies asrolling optimization problem, a model predictive control approach leads to anefficient history-dependent policy, which we call the short memory in thefuture (SMF) policy. Basically, the SMF policy leverages these memorylesspolicies to build an approximation of the Bellman value function. Numericalexperiments show the efficiency of our approach on benchmark instances from theliterature.

Future memories are not needed for large classes of POMDPs