We study the problem of best-arm identification with fixed budget in stochastic two-arm bandits with Bernoulli rewards. We prove that surprisingly, there is no algorithm that (i) performs as well as the algorithm sampling each arm equally (this algorithm is referred to as the {\it uniform sampling} algorithm) on all instances, and that (ii) strictly outperforms this algorithm on at least one instance. In short, there is no algorithm better than the uniform sampling algorithm. Towards this result, we introduce the natural class of {\it consistent} and {\it stable} algorithms, and show that any algorithm that performs as well as the uniform sampling algorithm on all instances belongs to this class. The proof is completed by deriving a lower bound on the error rate satisfied by any consistent and stable algorithm, and by showing that the uniform sampling algorithm matches this lower bound. Our results provide a solution to the two open problems presented in \cite{qin2022open}.

固定预算下的随机双臂赌博机最佳臂识别问题中，不存在优于均匀采样算法的算法，该问题的解决方案是引入一类称为“一致稳定算法”的自然算法，并证明该类算法与均匀采样算法的性能相同。

关于固定预算下二臂赌博机最优臂识别的统一最优算法