Adaptive Random Matrices in Gaussian Bandits: Spectral Universality and Selection-Induced Outliers
高斯多臂老虎机中的自适应随机矩阵:谱普适性与选择诱导的离群特征值
Adaptive arm selection changes the distribution of the observations collected by a bandit algorithm, but it need not change their limiting empirical spectrum. We study Gaussian bandit designs in which the dimension and the number of observations grow proportionally. A quantitative coupling theorem compares the design generated by any causal selection rule with an independent Gaussian design. If the logarithm of the number of available arms is sublinear in the dimension, the…