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 language | English |
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Journal | Advances in Neural Information Processing Systems |
Volume | 36 |
State | Published - 2023 |
Event | 37th Conference on Neural Information Processing Systems, NeurIPS 2023 - New Orleans, United States Duration: 10 Dec 2023 → 16 Dec 2023 |
Funding
Funders | Funder number |
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European Research Executive Agency | |
European Commission | 10139692 |
Israel Science Foundation | 2188 \ 20 |