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Journal Articles Journal of Machine Learning Research Year : 2021

Mixture Martingales Revisited with Applications to Sequential Tests and Confidence Intervals

Wouter M. Koolen
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Abstract

This paper presents new deviation inequalities that are valid uniformly in time under adaptive sampling in a multi-armed bandit model. The deviations are measured using the Kullback-Leibler divergence in a given one-dimensional exponential family, and may take into account several arms at a time. They are obtained by constructing for each arm a mixture martingale based on a hierarchical prior, and by multiplying those martingales. Our deviation inequalities allow us to analyze stopping rules based on generalized likelihood ratios for a large class of sequential identification problems, and to construct tight confidence intervals for some functions of the means of the arms.
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Dates and versions

hal-01886612 , version 1 (03-10-2018)
hal-01886612 , version 2 (27-11-2018)
hal-01886612 , version 3 (07-12-2021)

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Emilie Kaufmann, Wouter M. Koolen. Mixture Martingales Revisited with Applications to Sequential Tests and Confidence Intervals. Journal of Machine Learning Research, 2021. ⟨hal-01886612v3⟩
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