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Partially observable Markov decision processes (POMDPs) provide a modelingframework for autonomous decision making under uncertainty and imperfectsensing, e.g. robot manipulation and self-driving cars. However, optimalcontrol of POMDPs is notoriously intractable. This paper considers thequantitative problem of synthesizing sub-optimal stochastic finite statecontrollers (sFSCs) for POMDPs such that the probability of satisfying a set ofhigh-level specifications in terms of linear temporal logic (LTL) formulae ismaximized. We begin by casting the latter problem into an optimization and userelaxations based on the Poisson equation and McCormick envelopes. Then, wepropose an stochastic bounded policy iteration algorithm, leading to acontrolled growth in sFSC size and an any time algorithm, where the performanceof the controller improves with successive iterations, but can be stopped bythe user based on time or memory considerations. We illustrate the proposedmethod by a robot navigation case study.

Stochastic Finite State Control of POMDPs with LTL Specifications