Fixed-Budget Best Arm Identification with Variance-Dependent Regret Bounds
Primary Area: general machine learning (i.e., none of the above)
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Keywords: Best arm identification
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Abstract: We investigate the problem of fixed-budget best arm identification (BAI) for minimizing expected simple regret. In an adaptive experiment, a decision maker draws one of multiple treatment arms based on past observations and observes the outcome of the drawn arm. After the experiment, the decision maker recommends the treatment arm with the highest expected outcome. We evaluate the decision based on the expected simple regret, which is the difference between the expected outcomes of the best arm and the recommended arm. Due to inherent uncertainty, we evaluate the regret using the minimax criterion. First, we derive asymptotic lower bounds for the worst-case expected simple regret, which are characterized by the variances of potential outcomes (leading factor). Based on the lower bounds, we propose the Adaptive-Sampling (AS)-Augmented Inverse Probability Weighting (AIPW) strategy, which utilizes the AIPW estimator in recommending the best arm. Our theoretical analysis shows that the AS-AIPW strategy is asymptotically minimax optimal, meaning that the leading factor of its worst-case expected simple regret matches our derived worst-case lower bound. Finally, we validate the proposed method's effectiveness through simulation studies.
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Submission Number: 9273
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