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An Asymptotic Simplex Method and Markov Decision Processes

Summary: An Asymptotic Simplex Method and Markov
Decision Processes
Eitan Altman  , Konstantin Avrachenkov y , Jerzy Filar z
January 16, 2002
The purpose of this paper is twofold. First we present an asymp-
totic simplex method for the parametric linear programming. The
asymptotic simplex method allows to nd a solution which is optimal
for all suĂciently small values of the parameter. The present imple-
mentation of the asymptotic simplex method is based on the Laurent
series expansions and on the eĂcient use of the recurrent formulae for
the Laurent series coeĂcients. In the second part of the paper we ap-
ply the asymptotic simplex method to several models of the Markov
decision processes: computation of Blackwell optimal policies, Markov
branching decision chains, singularly perturbed MDPs and constrained
MDPs and stochastic games.
1 Introduction
The present paper consists of two parts. The rst part is devoted to the
asymptotic simplex method, which is designed to solve the parametric linear
program of the following form


Source: Avrachenkov, Konstantin - INRIA Sophia Antipolis


Collections: Computer Technologies and Information Sciences