LP based upper and lower bounds for Cesàro and Abel limits of the optimal values in problems of control of stochastic discrete time systems
Journal of Mathematical Analysis and Applications（2022）
Abstract
In this paper, we study asymptotic properties of problems of control of stochastic discrete time systems (also known as Markov decision processes) with time averaging and time discounting optimality criteria, and we establish that the Cesàro and Abel limits of the optimal values in such problems can be evaluated with the help of a certain infinite-dimensional linear programming problem and its dual.
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Key words
Stochastic optimal control,Markov decision processes (MDPs),Linear programming,Optimality conditions,Dynamic programming,Discrete time
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