Nonasymptotic sequential tests for overlapping hypotheses applied to near-optimal arm identification in bandit models

• Published in: Sequential analysis Vol. 40; no. 1; pp. 61 - 96
• Main Authors: Garivier, Aurélien, Kaufmann, Emilie
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 15.01.2021; Taylor & Francis Ltd
• Subjects: Best arm identification; Gaussian distribution; generalized likelihood ratio test; Hypotheses; Information theory; Likelihood ratio; Lower bounds; multi-armed bandits; Normal distribution; sequential testing; Statistical analysis

In this article, we study sequential testing problems with overlapping hypotheses. We first focus on the simple problem of assessing if the mean μ of a Gaussian distribution is smaller or larger than a fixed if both answers are considered to be correct. Then, we consider probably approximately corre...