We study the problem of best-arm identification (BAI) in the fixed-budget setting with heterogeneous reward variances. We propose two variance-adaptive BAI algorithms for this setting: SHVar for known reward variances and SHAdaVar for unknown reward variances. Our algorithms rely on non-uniform budget allocations among the arms where the arms with higher reward variances are pulled more often than those with lower variances. The main algorithmic novelty is in the design of SHAdaVar, which allocates budget greedily based on overestimating the unknown reward variances. We bound probabilities of misidentifying the best arms in both SHVar and SHAdaVar. Our analyses rely on novel lower bounds on the number of pulls of an arm that do not require closed-form solutions to the budget allocation problem. Since one of our budget allocation problems is analogous to the optimal experiment design with unknown variances, we believe that our results are of a broad interest. Our experiments validate our theory, and show that SHVar and SHAdaVar outperform algorithms from prior works with analytical guarantees.

研究在异质奖励方差的固定预算设置下的最佳臂识别问题，提出两种方差自适应的算法：SHVar和SHAdaVar，分别用于已知奖励方差和未知奖励方差情况下，通过不均匀预算分配实现对高方差臂的偏好，本文还给出了误判最佳臂的概率界限。

具有异质奖励方差的固定预算的最佳臂识别