Reinforcement Learning Based Algorithms for Average Cost Markov Decision Processes

2007 ◽  
Vol 17 (1) ◽  
pp. 23-52 ◽  
Author(s):  
Mohammed Shahid Abdulla ◽  
Shalabh Bhatnagar
Keyword(s):  
Reinforcement Learning ◽  
Markov Decision Processes ◽  
Average Cost ◽  
Decision Processes ◽  
Markov Decision

scholarly journals New discount and average optimality conditions for continuous-time Markov decision processes

2010 ◽  
Vol 42 (04) ◽  
pp. 953-985 ◽  
Author(s):  
Xianping Guo ◽  
Liuer Ye
Keyword(s):  
Markov Decision Processes ◽  
Continuous Time ◽  
Average Cost ◽  
Nonnegative Solution ◽  
Decision Processes ◽  
Stationary Policy ◽  
Discounted Cost ◽  
Markov Decision ◽  
Optimal Stationary Policy ◽  
Bounded Below

This paper deals with continuous-time Markov decision processes in Polish spaces, under the discounted and average cost criteria. All underlying Markov processes are determined by given transition rates which are allowed to be unbounded, and the costs are assumed to be bounded below. By introducing an occupation measure of a randomized Markov policy and analyzing properties of occupation measures, we first show that the family of all randomized stationary policies is ‘sufficient’ within the class of all randomized Markov policies. Then, under the semicontinuity and compactness conditions, we prove the existence of a discounted cost optimal stationary policy by providing a value iteration technique. Moreover, by developing a new average cost, minimum nonnegative solution method, we prove the existence of an average cost optimal stationary policy under some reasonably mild conditions. Finally, we use some examples to illustrate applications of our results. Except that the costs are assumed to be bounded below, the conditions for the existence of discounted cost (or average cost) optimal policies are much weaker than those in the previous literature, and the minimum nonnegative solution approach is new.

scholarly journals New discount and average optimality conditions for continuous-time Markov decision processes

2010 ◽  
Vol 42 (4) ◽  
pp. 953-985 ◽  
Author(s):  
Xianping Guo ◽  
Liuer Ye
Keyword(s):  
Markov Decision Processes ◽  
Continuous Time ◽  
Average Cost ◽  
Nonnegative Solution ◽  
Decision Processes ◽  
Stationary Policy ◽  
Discounted Cost ◽  
Markov Decision ◽  
Optimal Stationary Policy ◽  
Bounded Below

This paper deals with continuous-time Markov decision processes in Polish spaces, under the discounted and average cost criteria. All underlying Markov processes are determined by given transition rates which are allowed to be unbounded, and the costs are assumed to be bounded below. By introducing an occupation measure of a randomized Markov policy and analyzing properties of occupation measures, we first show that the family of all randomized stationary policies is ‘sufficient’ within the class of all randomized Markov policies. Then, under the semicontinuity and compactness conditions, we prove the existence of a discounted cost optimal stationary policy by providing a value iteration technique. Moreover, by developing a new average cost, minimum nonnegative solution method, we prove the existence of an average cost optimal stationary policy under some reasonably mild conditions. Finally, we use some examples to illustrate applications of our results. Except that the costs are assumed to be bounded below, the conditions for the existence of discounted cost (or average cost) optimal policies are much weaker than those in the previous literature, and the minimum nonnegative solution approach is new.

Approximation of average cost optimal policies for general Markov decision processes with unbounded costs

1997 ◽  
Vol 45 (2) ◽  
pp. 245-263
Author(s):  
Evgueni Gordienko ◽  
Ra�l Montes-De-Oca ◽  
Adolfo Minj�rez-Sosa
Keyword(s):  
Markov Decision Processes ◽  
Average Cost ◽  
Decision Processes ◽  
Optimal Policies ◽  
Markov Decision
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