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How Does Variance Shape the Regret in Contextual Bandits?
Zeyu Jia, Jian Qian, Alexander Rakhlin +1
We consider realizable contextual bandits with general function approximation, investigating how small reward variance can lead to better-than-minimax regret bounds. Unlike in mini…
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…
Assouad, Fano, and Le Cam with Interaction: A Unifying Lower Bound Framework and Characterization for Bandit Learnability
Fan Chen, Dylan J. Foster, Yanjun Han +3
We develop a unifying framework for information-theoretic lower bound in statistical estimation and interactive decision making. Classical lower bound techniques -- such as Fano's…
Offline Oracle-Efficient Learning for Contextual MDPs via Layerwise Exploration-Exploitation Tradeoff
Jian Qian, Haichen Hu, David Simchi-Levi
Motivated by the recent discovery of a statistical and computational reduction from contextual bandits to offline regression (Simchi-Levi and Xu, 2021), we address the general (sto…
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…