Information Theoretic Lower Bounds for Information Theoretic Upper Bounds

Roi Livni*

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

Abstract

We examine the relationship between the mutual information between the output model and the empirical sample and the generalization of the algorithm 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.

Original languageEnglish
JournalAdvances in Neural Information Processing Systems
Volume36
StatePublished - 2023
Event37th Conference on Neural Information Processing Systems, NeurIPS 2023 - New Orleans, United States
Duration: 10 Dec 202316 Dec 2023

Funding

FundersFunder number
Google
European Research Executive Agency
European Research Council10139692
European Research Council
Israel Science Foundation2188 \ 20
Israel Science Foundation

    Fingerprint

    Dive into the research topics of 'Information Theoretic Lower Bounds for Information Theoretic Upper Bounds'. Together they form a unique fingerprint.

    Cite this