aiqbench analysis
This research presents a unified adaptive strategy for best-arm identification that is proven to be simultaneously asymptotically minimax and Bayes optimal. By solving a Gaussian minimax game within a two-stage sampling framework, the authors establish tight upper bounds on simple regret that match theoretical lower limits without requiring prior knowledge of outcome distributions. This work advances fundamental understanding in multi-armed bandit theory with direct implications for efficient resource allocation algorithms driven by machine learning principles.
Minimax and Bayes Optimal Best-Arm Identification
arXiv:2506.24007v5 Announce Type: replace-cross Abstract: This study investigates minimax and Bayes optimal strategies for fixed-budget best-arm identification. We consider an adaptive procedure consisting of a sampling phase followed by a recommendation phase, and we design an adaptive experiment within this framework to efficiently identify the best arm, defined as the one with the highest expected outcome. In our proposed strategy, the sampling phase consists of two stages. The first stage is a pilot phase, in which we allocate samples uniformly across arms to eliminate clearly suboptimal arms and to estimate outcome variances. Before entering the second stage, we solve a Gaussian minimax game, which yields a sampling policy and a decision rule. In the second stage, samples are allocated according to this policy. After the sampling phase, the procedure enters the recommendation phase, where we select an arm using the decision rule. We prove that this single strategy is simultaneously asymptotically minimax and Bayes optimal for the simple regret, and we establish upper bounds that coincide exactly with our lower bounds, including the constant terms. The lower bounds hold against every adaptive experiment and for every fixed number of arms, and the strategy attains them without knowing the outcome distributions or the prior.
Abstract:This study investigates minimax and Bayes optimal strategies for fixed-budget best-arm identification. We consider an adaptive procedure consisting of a sampling phase followed by a recommendation phase, and we design an adaptive experiment within this framework to efficiently identify the best arm, defined as the one with the highest expected outcome. In our proposed strategy, the sampling phase consists of two stages. The first stage is a pilot phase, in which we allocate samples uniformly across arms to eliminate clearly suboptimal arms and to estimate outcome variances. Before entering the second stage, we solve a Gaussian minimax game, which yields a sampling policy and a decision rule. In the second stage, samples are allocated according to this policy. After the sampling phase, the procedure enters the recommendation phase, where we select an arm using the decision rule. We prove that this single strategy is simultaneously asymptotically minimax and Bayes optimal for the simple regret, and we establish upper bounds that coincide exactly with our lower bounds, including the constant terms. The lower bounds hold against every adaptive experiment and for every fixed number of arms, and the strategy attains them without knowing the outcome distributions or the prior.
Econometrics (econ.EM); Machine Learning (cs.LG); Statistics Theory (math.ST); Methodology (stat.ME); Machine Learning (stat.ML)
arXiv:2506.24007 [econ.EM]
(or arXiv:2506.24007v5 [econ.EM] for this version)
Full text under the publisher's open licence · 219 words
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