Information Theoretic Lower Bounds for Information Theoretic Upper Bounds

Roi Livni

Keywords: Learning Theory

TL;DR: Every learner in stochastic convex optimization must carry dimension dependent bits of information over the data set

Abstract: We examine the relationship between the mutual information between the output model and the empirical sample and the algorithm's generalization in the context of stochastic convex optimization. Despite increasing interest in information-theoretic generalization bounds, it is uncertain if these bounds can provide insight into the exceptional performance of various learning algorithms. Our study of stochastic convex optimization reveals that, for true risk minimization, dimension-dependent mutual information is necessary. This indicates that existing information-theoretic generalization bounds fall short in capturing the generalization capabilities of algorithms like SGD and regularized ERM, which have dimension-independent sample complexity.

Submission Number: 6254