Exact solution of the Bellman equation for a β-discounted reward in a two-armed bandit with switching arms

Donchev, Doncho S.

doi:https://doi.org/10.1155/S1048953399000155

International Journal of Stochastic Analysis

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Volume 12 |Article ID 924375 | https://doi.org/10.1155/S1048953399000155

Doncho S. Donchev, "Exact solution of the Bellman equation for a β-discounted reward in a two-armed bandit with switching arms", International Journal of Stochastic Analysis, vol. 12, Article ID 924375, 10 pages, 1999. https://doi.org/10.1155/S1048953399000155

Exact solution of the Bellman equation for a β-discounted reward in a two-armed bandit with switching arms

Doncho S. Donchev¹

¹Higher Institute of Food and Flavor Industries, 26, Maritza str., Plovdiv 4002, Bulgaria

Received01 May 1998

Revised01 Oct 1998

Abstract

We consider the symmetric Poissonian two-armed bandit problem. For the case of switching arms, only one of which creates reward, we solve explicitly the Bellman equation for a β-discounted reward and prove that a myopic policy is optimal.

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Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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