Explicit upper bounds on filter-kernel sensitivity and POMDP value differences in terms of Wasserstein and total-variation distances between transition and observation kernels, with decaying error bounds for joint state-measurement quantization.
Partially Observed Optimal Stochastic Control: Regularity, Optimality, Approximations, and Learning
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abstract
In this review/tutorial article, we present recent progress on optimal control of partially observed Markov Decision Processes (POMDPs). We first present regularity and continuity conditions for POMDPs and their belief-MDP reductions, where these constitute weak Feller and Wasserstein regularity and controlled filter stability. These are then utilized to arrive at existence results on optimal policies for both discounted and average cost problems, and regularity of value functions. Then, we study rigorous approximation results involving quantization based finite model approximations as well as finite window approximations under controlled filter stability. Finally, we present several recent reinforcement learning theoretic results which rigorously establish convergence to near optimality under both criteria.
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Sensitivity of Filter Kernels and Robustness Bounds to Transition and Measurement Kernel Perturbations in Partially Observable Stochastic Control
Explicit upper bounds on filter-kernel sensitivity and POMDP value differences in terms of Wasserstein and total-variation distances between transition and observation kernels, with decaying error bounds for joint state-measurement quantization.