Optimization of Discounted Markov Decision Problems

1969 ◽  
Vol 20 (4) ◽  
pp. 499-500 ◽  
Author(s):  
N. A. J. Hastings
Keyword(s):  
Decision Problems ◽  
Markov Decision Problems ◽  
Markov Decision

Geometric convergence of value-iteration in multichain Markov decision problems

1979 ◽  
Vol 11 (01) ◽  
pp. 188-217 ◽  
Author(s):  
P. J. Schweitzer ◽  
A. Federgruen
Keyword(s):  
Convergence Rate ◽  
Iteration Method ◽  
Chain Structure ◽  
Decision Problems ◽  
Value Iteration ◽  
Convergence Factor ◽  
Markov Decision Problems ◽  
Geometric Convergence ◽  
Markov Decision ◽  
Maximal Gain

This paper considers undiscounted Markov decision problems. With no restriction (on either the periodicity or chain structure of the problem) we show that the value iteration method for finding maximal gain policies exhibits a geometric rate of convergence, whenever convergence occurs. In addition, we study the behaviour of the value-iteration operator; we give bounds for the number of steps needed for contraction, describe the ultimate behaviour of the convergence factor and give conditions for the existence of a uniform convergence rate.

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