Fatou's Lemma in Its Classical Form and Lebesgue's Convergence Theorems for Varying Measures with Applications to Markov Decision Processes

2020 ◽  
Vol 65 (2) ◽  
pp. 270-291 ◽  
Author(s):  
E. A. Feinberg ◽  
P. O. Kasyanov ◽  
Y. Liang
Keyword(s):  
Markov Decision Processes ◽  
Decision Processes ◽  
Convergence Theorems ◽  
Classical Form ◽  
Markov Decision ◽  
Fatou’S Lemma ◽  
Fatou's Lemma

Extreme-point solutions in Markov decision processes

1983 ◽  
Vol 20 (04) ◽  
pp. 835-842
Author(s):  
David Assaf
Keyword(s):  
Convex Function ◽  
Extreme Point ◽  
Markov Decision Processes ◽  
Convex Functions ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
Markov Decision ◽  
Full Solution

The paper presents sufficient conditions for certain functions to be convex. Functions of this type often appear in Markov decision processes, where their maximum is the solution of the problem. Since a convex function takes its maximum at an extreme point, the conditions may greatly simplify a problem. In some cases a full solution may be obtained after the reduction is made. Some illustrative examples are discussed.

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