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Asymptotically efficient adaptive allocation schemes for controlled Markov chains: finite parameter space

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3 Author(s)
Agrawal, R. ; Dept. of Electr. & Comput. Sci., Michigan Univ., Ann Arbor, MI, USA ; Teneketzis, D. ; Anantharam, V.

The authors consider a controlled Markov chain whose transition probabilities and initial distribution are parameterized by an unknown parameter θ to some known parameter space Θ. There is a one-step reward associated with each pair of control and following state of the process. The objective is to maximize the expected value of the sum of one-step rewards over an infinite horizon. By introducing the loss associated with a control scheme, the authors show that the problem is equivalent to minimizing the loss. They define uniformly good adaptive control schemes and restrict attention to these schemes. They develop a lower bound on the loss associated with any uniformly good control scheme. Finally, they construct an adaptive control scheme whose loss equals the lower bound and is therefore optimal

Published in:

Decision and Control, 1988., Proceedings of the 27th IEEE Conference on

Date of Conference:

7-9 Dec 1988