Infinite horizon average cost dynamic programming subject to ambiguity on conditional distribution
Charalambous, Charalambos D.
PublisherInstitute of Electrical and Electronics Engineers Inc.
SourceProceedings of the IEEE Conference on Decision and Control
Proceedings of the IEEE Conference on Decision and Control
Volume54rd IEEE Conference on Decision and Control,CDC 2015
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This paper addresses the optimality of stochastic control strategies based on the infinite horizon average cost criterion, subject to total variation distance ambiguity on the conditional distribution of the controlled process. This stochastic optimal control problem is formulated using minimax theory, in which the minimization is over the control strategies and the maximization is over the conditional distributions. Under the assumption that, for every stationary Markov control law the maximizing conditional distribution of the controlled process is irreducible, we derive a new dynamic programming recursion which minimizes the future ambiguity, and we propose a new policy iteration algorithm. The new dynamic programming recursion includes, in addition to the standard terms, the oscillator semi-norm of the cost-to-go. The maximizing conditional distribution is found via a water-filling algorithm. The implications of our results are demonstrated through an example. © 2015 IEEE.
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