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。