Bridging the gap between regret minimization and best arm identification, with application to A/B tests
This work addresses the gap between two key objectives in online learning for practitioners in fields such as website testing and clinical trials, though it appears incremental by merging existing approaches.
The paper tackles the problem of simultaneously achieving regret minimization and best arm identification in online learning, providing theoretical analysis for algorithms that are delta-PAC with guaranteed decision time bounds, and extends results to non-iid cases. It offers a technique for balancing cost and decision time in adaptive tests like A/B testing and clinical trials.
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.