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Self-Normalized Martingales and Uniform Regret Bounds for Linear Regression
Fan Chen, Jian Qian, Alexander Rakhlin +1
Self-normalized martingale inequalities lie at the heart of confidence ellipsoids for online least squares and, more broadly, many bandit and reinforcement-learning results. Yet ex…
Evolution of Information in Interactive Decision Making: A Case Study for Multi-Armed Bandits
Yuzhou Gu, Yanjun Han, Jian Qian
We study the evolution of information in interactive decision making through the lens of a stochastic multi-armed bandit problem. Focusing on a fundamental example where a unique o…
Refined Risk Bounds for Unbounded Losses via Transductive Priors
Jian Qian, Alexander Rakhlin, Nikita Zhivotovskiy
We revisit the sequential variants of linear regression with the squared loss, classification problems with hinge loss, and logistic regression, all characterized by unbounded loss…
Online Estimation via Offline Estimation: An Information-Theoretic Framework
Dylan J. Foster, Yanjun Han, Jian Qian +1
The classical theory of statistical estimation aims to estimate a parameter of interest under data generated from a fixed design ("offline estimation"), while the contemporary t…