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arXiv · 2003.01328

Bounded Regret for Finitely Parameterized Multi-Armed Bandits

Kishan Panaganti·Dileep Kalathil
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Abstract

We consider the problem of finitely parameterized multi-armed bandits where the model of the underlying stochastic environment can be characterized based on a common unknown parameter. The true parameter is unknown to the learning agent. However, the set of possible parameters, which is finite, is known a priori. We propose an algorithm that is simple and easy to implement, which we call Finitely Parameterized Upper Confidence Bound (FP-UCB) algorithm, which uses the information about the underlying parameter set for faster learning. In particular, we show that the FP-UCB algorithm achieves a bounded regret under some structural condition on the underlying parameter set. We also show that, if the underlying parameter set does not satisfy the necessary structural condition, the FP-UCB algorithm achieves a logarithmic regret, but with a smaller preceding constant compared to the standard UCB algorithm. We also validate the superior performance of the FP-UCB algorithm through extensive numerical simulations.

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BibTeXRIS

Kishan Panaganti, Dileep Kalathil. 2020-11-07. Bounded Regret for Finitely Parameterized Multi-Armed Bandits. https://doi.org/10.1109/lcsys.2020.3008798

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