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Fourth-Moment Geometry of Rademacher Sums
Peigan Gao, Jian Qian
Let be independent Rademacher signs and let satisfy the normalization below. For the normalized Rademacher sum, we…
An Optimal Agnostic PAC Algorithm
Markus Engelund Mathiasen, Jian Qian, Nikita Zhivotovskiy
Let be a class of finite VC dimension . Writing for the binary risk and , we construct a learner achieving the statistical…
Multiplicative Oracle Inequalities for Transductive Learning via Level-Set Aggregation
Jian Qian, Jiachen Xu
We revisit transductive learning where predictions are made with the set of all covariates known in advance. In the leave-one-out (LOO) setting, the prediction is made with labels…
Achieving Optimal Static and Dynamic Regret Simultaneously in Bandits with Deterministic Losses
Jian Qian, Chen-Yu Wei
In adversarial multi-armed bandits, two performance measures are commonly used: static regret, which compares the learner to the best fixed arm, and dynamic regret, which compares…
Data Reconstruction: Identifiability and Optimization with Sample Splitting
Yujie Shen, Zihan Wang, Jian Qian +1
Training data reconstruction from KKT conditions has shown striking empirical success, yet it remains unclear when the resulting KKT equations have unique solutions and, even in id…
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…
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…