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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…
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…
Ratio Covers of Convex Sets and Optimal Mixture Density Estimation
Spencer Compton, Gábor Lugosi, Jaouad Mourtada +2
We study density estimation in Kullback-Leibler divergence: given an i.i.d. sample from an unknown density , the goal is to construct an estimator such that…
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…