Eugene A. Feinberg, Mark E. Lewis
Published 2015-07-17Version 1
This paper describes results on the existence of optimal policies and convergence properties of optimal actions for discounted and average-cost Markov Decision Processes with weakly continuous transition probabilities. It is possible that cost functions are unbounded and action sets are not compact. The results are applied to stochastic periodic-review inventory control problems, for which they imply the existence of stationary optimal policies and certain optimality properties. The optimality of $(s,S)$ policies is proved by using dynamic programming equations for discounted costs and the vanishing discount factor approach for average costs per unit time.
Average-Cost Markov Decision Processes with Weakly Continuous Transition Probabilities
On the Minimum Pair Approach for Average-Cost Markov Decision Processes with Countable Discrete Action Space and Strictly Unbounded Costs
Markov Decision Processes with Incomplete Information and Semi-Uniform Feller Transition Probabilities
![QR code for arXiv:1507.05125 [math.OC]](http://oss.arxitics.com/images/favicon.svg)