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arXiv · 1710.02869

An Analysis of the Value of Information when Exploring Stochastic, Discrete Multi-Armed Bandits

Isaac J. Sledge·Jose C. Principe
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Abstract

In this paper, we propose an information-theoretic exploration strategy for stochastic, discrete multi-armed bandits that achieves optimal regret. Our strategy is based on the value of information criterion. This criterion measures the trade-off between policy information and obtainable rewards. High amounts of policy information are associated with exploration-dominant searches of the space and yield high rewards. Low amounts of policy information favor the exploitation of existing knowledge. Information, in this criterion, is quantified by a parameter that can be varied during search. We demonstrate that a simulated-annealing-like update of this parameter, with a sufficiently fast cooling schedule, leads to an optimal regret that is logarithmic with respect to the number of episodes.

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Isaac J. Sledge, Jose C. Principe. 2018-03-03. An Analysis of the Value of Information when Exploring Stochastic, Discrete Multi-Armed Bandits. https://doi.org/10.3390/e20030155

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