Papers › Minimax Optimal Algorithms for Fixed-Budget Best Arm Identification

Minimax Optimal Algorithms for Fixed-Budget Best Arm Identification

9 Jun 2022arXiv:2206.04646archive 2025-07-28

Junpei Komiyama, Taira Tsuchiya, Junya Honda

We consider the fixed-budget best arm identification problem where the goal is to find the arm of the largest mean with a fixed number of samples. It is known that the probability of misidentifying the best arm is exponentially small to the number of rounds. However, limited characterizations have been discussed on the rate (exponent) of this value. In this paper, we characterize the minimax optimal rate as a result of an optimization over all possible parameters. We introduce two rates, Rᵍᵒ and Rᵍᵒ_∞, corresponding to lower bounds on the probability of misidentification, each of which is associated with a proposed algorithm. The rate Rᵍᵒ is associated with Rᵍᵒ-tracking, which can be efficiently implemented by a neural network and is shown to outperform existing algorithms. However, this rate requires a nontrivial condition to be achievable. To address this issue, we introduce the second rate Rᵍᵒ_∞. We show that this rate is indeed achievable by introducing a conceptual algorithm called delayed optimal tracking (DOT).

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