4 papers · 1 filter
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…
Characterizing Online and Private Learnability under Distributional Constraints via Generalized Smoothness
Moïse Blanchard, Abhishek Shetty, Alexander Rakhlin
Understanding minimal assumptions that enable learning and generalization is perhaps the central question of learning theory. Several celebrated results in statistical learning the…
A Gapped Scale-Sensitive Dimension and Lower Bounds for Offset Rademacher Complexity
Zeyu Jia, Yury Polyanskiy, Alexander Rakhlin
We study gapped scale-sensitive dimensions of a function class in both sequential and non-sequential settings. We demonstrate that covering numbers for any uniformly bounded class…
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…