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Bridging the gap between regret minimization and best arm identification, with application to A/B tests

Abstract : State of the art online learning procedures focus either on selecting the best alternative ("best arm identification") or on minimizing the cost (the "regret"). We merge these two objectives by providing the theoretical analysis of cost minimizing algorithms that are also delta-PAC (with a proven guaranteed bound on the decision time), hence fulfilling at the same time regret minimization and best arm identification. This analysis sheds light on the common observation that ill-callibrated UCB-algorithms minimize regret while still identifying quickly the best arm. We also extend these results to the non-iid case faced by many practitioners. This provides a technique to make cost versus decision time compromise when doing adaptive tests with applications ranging from website A/B testing to clinical trials.
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https://hal.archives-ouvertes.fr/hal-02457477
Contributor : Clément Calauzènes <>
Submitted on : Tuesday, January 28, 2020 - 10:26:15 AM
Last modification on : Thursday, April 15, 2021 - 3:31:45 AM

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  • HAL Id : hal-02457477, version 1
  • ARXIV : 1810.04088

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Rémy Degenne, Thomas Nedelec, Clément Calauzènes, Vianney Perchet. Bridging the gap between regret minimization and best arm identification, with application to A/B tests. AISTATS 2019 - 22nd International Conference on Artificial Intelligence and Statistics, Apr 2019, Okinawa, Japan. ⟨hal-02457477⟩

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