2026.06.03 Colloquia Seminars
| Speaker |
张存惠教授，罗格斯大学 |
| Title |
Precise Regret and Adaptive Inference in Multi-Armed Bandits |
| Time |
2026.06.08 11:00-12:00 |
| Venue |
N533 |
| Abstract |
Despite extensive research over the widely used UCB algorithms in multi-armed bandits, a precise understanding of their regret behavior remains elusive. This gap has not only hindered the evaluation of their actual algorithmic efficiency, but also limited further developments in statistical inference in sequential experiments. We bridge these fundamental aspects through a deterministic characterization of the number of arm pulls for an UCB index algorithm. The resulting precise regret formula not only accurately captures the actual behavior of the UCB algorithm for finite time horizons and individual problem instances, but also provides significant new insights into the regimes not covered by existing theoretical frameworks. The deterministic characterization of the number of arm pulls for the UCB algorithm also has major implications in adaptive statistical inference. We show that the UCB algorithm satisfies certain ‘stability’ properties that lead to quantitative central limit theorems in two settings: for the empirical means of unknown rewards in the bandit setting, and for a class of Ridge estimators when the arm means exhibit a structured relationship through covariates. Our technical approach relies on an application of a new comparison principle between the UCB algorithm and its noiseless, continuous-time minimax counterpart. We expect this new principle to be broadly applicable for general UCB index algorithms. This talk is based on joint work with Qiyang Han and Koulik Khamaru. |
| Biography |
Cun-Hui Zhang, Distinguished Professor of Statistics at Rutgers University, is a Fellow of the Institute of Mathematical Statistics and a Fellow of American Statistical Association. His research interests include high-dimensional data, machine learning, empirical Bayes, time series, nonparametric methods, multivariate analysis, survival data and biostatistics, functional MRI, closed loop diabetes control, and network tomography. | |
