TY - JOUR

T1 - Strong polynomiality of the Gass-Saaty shadow-vertex pivoting rule for controlled random walks

AU - Even, Guy

AU - Zadorojniy, Alexander

PY - 2012/12

Y1 - 2012/12

N2 - We consider the subclass of linear programs that formulate Markov Decision Processes (mdps). We show that the Simplex algorithm with the Gass-Saaty shadow-vertex pivoting rule is strongly polynomial for a subclass of mdps, called controlled random walks (CRWs); the running time is O({pipe}S{pipe}3{dot operator}{pipe}U{pipe}2), where {pipe}S{pipe} denotes the number of states and {pipe}U{pipe} denotes the number of actions per state. This result improves the running time of Zadorojniy et al. (Mathematics of Operations Research 34(4):992-1007, 2009) algorithm by a factor of {pipe}S{pipe}. In particular, the number of iterations needed by the Simplex algorithm for CRWs is linear in the number of states and does not depend on the discount factor.

AB - We consider the subclass of linear programs that formulate Markov Decision Processes (mdps). We show that the Simplex algorithm with the Gass-Saaty shadow-vertex pivoting rule is strongly polynomial for a subclass of mdps, called controlled random walks (CRWs); the running time is O({pipe}S{pipe}3{dot operator}{pipe}U{pipe}2), where {pipe}S{pipe} denotes the number of states and {pipe}U{pipe} denotes the number of actions per state. This result improves the running time of Zadorojniy et al. (Mathematics of Operations Research 34(4):992-1007, 2009) algorithm by a factor of {pipe}S{pipe}. In particular, the number of iterations needed by the Simplex algorithm for CRWs is linear in the number of states and does not depend on the discount factor.

KW - Controlled queues

KW - Controlled random walks

KW - Gass-Saaty shadow-vertex pivoting rule

KW - Markov decision process

KW - Simplex algorithm

UR - http://www.scopus.com/inward/record.url?scp=84870505898&partnerID=8YFLogxK

U2 - 10.1007/s10479-012-1199-x

DO - 10.1007/s10479-012-1199-x

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AN - SCOPUS:84870505898

SN - 0254-5330

VL - 201

SP - 159

EP - 167

JO - Annals of Operations Research

JF - Annals of Operations Research

IS - 1

ER -