On the Existence of a Complexity in Fixed Budget Bandit Identification

• URL: http://arxiv.org/abs/2303.09468v2
• Date: Fri, 30 Jun 2023 09:42:18 GMT
• Title: On the Existence of a Complexity in Fixed Budget Bandit Identification
• Authors: R\'emy Degenne
• Abstract summary: In fixed budget bandit identification, an algorithm sequentially observes samples from several distributions up to a given final time. We show that there is no such complexity for several fixed budget identification tasks including Bernoulli best arm identification with two arms.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In fixed budget bandit identification, an algorithm sequentially observes samples from several distributions up to a given final time. It then answers a query about the set of distributions. A good algorithm will have a small probability of error. While that probability decreases exponentially with the final time, the best attainable rate is not known precisely for most identification tasks. We show that if a fixed budget task admits a complexity, defined as a lower bound on the probability of error which is attained by the same algorithm on all bandit problems, then that complexity is determined by the best non-adaptive sampling procedure for that problem. We show that there is no such complexity for several fixed budget identification tasks including Bernoulli best arm identification with two arms: there is no single algorithm that attains everywhere the best possible rate.

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