Average optimality for continuous-time Markov decision processes under weak continuity conditions

This article considers the average optimality for a continuous-time Markov decision process with Borel state and action spaces and an arbitrarily unbounded nonnegative cost rate. The existence of a deterministic stationary optimal policy is proved under a different and general set of conditions as compared to the previous literature; the controlled process can be explosive, the transition rates can be arbitrarily unbounded and are weakly continuous, the multifunction defining the admissible action spaces can be neither compact-valued nor upper semi-continuous, and the cost rate is not necessarily inf-compact

Verification of Uncertain POMDPs Using Barrier Certificates

We consider a class of partially observable Markov decision processes (POMDPs) with uncertain transition and/or observation probabilities. The uncertainty takes the form of probability intervals. Such uncertain POMDPs can be used, for example, to model autonomous agents with sensors with limited accuracy, or agents undergoing a sudden component failure, or structural damage [1]. Given an uncertain POMDP representation of the autonomous agent, our goal is to propose a method for checking whether the system will satisfy an optimal performance, while not violating a safety requirement (e.g. fuel level, velocity, and etc.). To this end, we cast the POMDP problem into a switched system scenario. We then take advantage of this switched system characterization and propose a method based on barrier certificates for optimality and/or safety verification. We then show that the verification task can be carried out computationally by sum-of-squares programming. We illustrate the efficacy of our method by applying it to a Mars rover exploration example.Comment: 8 pages, 4 figure