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 …

The problem of sequential vector quantization of a stationary Markov source is cast as an
equivalent stochastic control problem with partial observations. This problem is analyzed …

Control and optimization of dynamical systems in the presence of stochastic uncertainty is a
mature field with a large range of applications. A comprehensive treatment of such problems …

The average cost optimality is known to be a challenging problem for partially observable
stochastic control, with few results available beyond the finite state, action, and …

We propose a probabilistic numerical method based on optimal quantization to solve some
multi-dimensional stochastic control problems that arise, for example, in mathematical …

This paper deals with control of partially observable discrete-time stochastic systems. It
introduces and studies Markov Decision Processes with Incomplete Information and with …

We consider the average cost problem for partially observable Markov decision processes
(POMDP) with finite state, observation, and control spaces. We prove that there exists an ε …

The value function for the average cost control of a class of partially observed Markov chains
is derived as the" vanishing discount limit," in a suitable sense, of the value functions for the …

We consider the problem of minimizing a certainty equivalent of the total or discounted cost
over a finite and an infinite time horizon that is generated by a partially observable Markov …

This paper studies weak continuity of nonlinear filters. It is well-known that Borel
measurability of transition probabilities for problems with incomplete state observations is …