Adaptive Random Matrices in Gaussian Bandits: Spectral Universality and Selection-Induced Outliers
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 empirical spectral distribution converges to the Marchenko-Pastur law, uniformly over the selection rule. Consequently, Gaussian Bayesian bandits have policy-independent first-order limits for posterior mean-square unc...
| Authors | Sudarshan Manikantan, Abhishek Bhattacharjee |
|---|---|
| Primary category | stat.ML |
| Published | 23 September 2026 |
| Last updated at source | 23 September 2026 |
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