A superharmonic approach to solving infinite horizon partially observable Markov decision problems

1995 ◽  
Vol 41 (1) ◽  
pp. 71-88 ◽  
Author(s):  
D. J. White
Keyword(s):  
Infinite Horizon ◽  
Decision Problems ◽  
Markov Decision Problems ◽  
Markov Decision ◽  
Partially Observable Markov ◽  
Partially Observable

PARTIALLY OBSERVABLE MARKOV DECISION PROCESSES AND PERIODIC POLICIES WITH APPLICATIONS

2011 ◽  
Vol 10 (06) ◽  
pp. 1175-1197 ◽  
Author(s):  
JOHN GOULIONIS ◽  
D. STENGOS
Keyword(s):  
Markov Decision Processes ◽  
Piecewise Linear ◽  
Linear Equations ◽  
Infinite Horizon ◽  
Decision Processes ◽  
Value Functions ◽  
Discounted Cost ◽  
Markov Decision ◽  
Partially Observable Markov ◽  
Partially Observable

This paper treats the infinite horizon discounted cost control problem for partially observable Markov decision processes. Sondik studied the class of finitely transient policies and showed that their value functions over an infinite time horizon are piecewise linear (p.w.l) and can be computed exactly by solving a system of linear equations. However, the condition for finite transience is stronger than is needed to ensure p.w.l. value functions. In this paper, we introduce alternatively the class of periodic policies whose value functions turn out to be also p.w.l. Moreover, we examine a more general condition than finite transience and periodicity that ensures p.w.l. value functions. We implement these ideas in a replacement problem under Markovian deterioration, investigate for periodic policies and give numerical examples.

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