The Multi-Armed Bandit Problem: An Efficient Non-Parametric Solution

Hock Peng Chan

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arXiv · 1703.08285

The Multi-Armed Bandit Problem: An Efficient Non-Parametric Solution

Hock Peng Chan

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Abstract

Lai and Robbins (1985) and Lai (1987) provided efficient parametric solutions to the multi-armed bandit problem, showing that arm allocation via upper confidence bounds (UCB) achieves minimum regret. These bounds are constructed from the Kullback-Leibler information of the reward distributions, estimated from specified parametric families. In recent years there has been renewed interest in the multi-armed bandit problem due to new applications in machine learning algorithms and data analytics. Non-parametric arm allocation procedures like $\epsilon$-greedy, Boltzmann exploration and BESA were studied, and modified versions of the UCB procedure were also analyzed under non-parametric settings. However unlike UCB these non-parametric procedures are not efficient under general parametric settings. In this paper we propose efficient non-parametric procedures.

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Hock Peng Chan. 2017-03-24. The Multi-Armed Bandit Problem: An Efficient Non-Parametric Solution. https://arxiv.org/abs/1703.08285

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