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ZOR -MathematicalMethodsofOperationsResearch(1995)42:169-188 g ~ i il The LinearProgram Approachin Multi-Chain Markov
 

Summary: ZOR - MathematicalMethodsofOperationsResearch(1995)42:169-188 g ~ i il
The LinearProgram Approachin Multi-Chain Markov
Decision Processes Revisited
EITANALTMAN
INRIA,CentreSophiaAntipolis,06565ValbonneCedex,France
FLOS SPIEKSMA
Institute ofMathematics& ComputerScience,UniversityofLeiden,P.O.Box9512,
2300RALeiden,The Netherlands
Abstract: LinearProgrammingis knownto be an important and usefultool for solvingMarkov
Decision Processes(MDP). its derivationrelies on the DynamicProgrammingapproach,which
also servesto solveMDP. However,for Markov DecisionProcesseswith severalconstraints the
only available methods are based on Linear Programs.The aim of this paper is to investigate
someaspectsofsuchLinearPrograms,relatedto multi-chainMDPs.Wefirstpresenta stochastic
interpretation ofthe decisionvariablesthat appear in the LinearProgramsavailablein the litera-
ture. We then showfor the multi-constrainedMarkovDecisionProcessthat the Linear Program
suggestedin [9] can be obtainedfrom an equivalentunconstrainedLagrangeformulationof the
control problem. This shows the connection between the Linear Program approach and the
Lagrangeapproach,that waspreviouslyusedonlyfor the caseofa singleconstraint[3, 14, 15].
Key Words: Multi-chain Markov Decision Processes, average cost criterion, state-action fre-
quencies,deviationmeasure,linearprogramming,lagrangeformulation.

  

Source: Altman, Eitan.- Projet Maestro, Université de Nice Sophia Antipolis

 

Collections: Engineering