Summary: Asymptotic Linear Programming and Policy
Improvement for Singularly Perturbed Markov
Eitan Altman \Lambda Konstantin E. Avrachenkov y Jerzy A. Filar z
In this paper we consider a singularly perturbed Markov decision
process with finitely many states and actions and the limiting expected
average reward criterion. We make no assumptions about the under
lying ergodic structure. We present algorithms for the computation
of a uniformly optimal deterministic control, that is, a control which
is optimal for all values of the perturbation parameter that are suf
ficiently small. Our algorithms are based on Jeroslow's Asymptotic
Key Words: Markov Decision Processes, Singular Perturbations,
Asymptotic Linear Programming.
Running title: Asymptotic Linear Programming for Singularly
Singularly perturbed Markov decision processes (MDPs, for short), are dy
namic stochastic systems controlled by a ''controller'' or a ''decisionmaker''