Information Theoretic Lower Bounds for Information Theoretic Upper Bounds

• URL: http://arxiv.org/abs/2302.04925v2
• Date: Sun, 14 Jan 2024 08:18:25 GMT
• Title: Information Theoretic Lower Bounds for Information Theoretic Upper Bounds
• Authors: Roi Livni
• Abstract summary: We examine the relationship between the output model and the empirical generalization and the algorithm in the context of convex optimization. Our study reveals that, for true risk minimization, mutual information is necessary. Existing information-theoretic generalization bounds fall short in capturing the capabilities of algorithms like SGD and regularized, which have-independent dimension sample complexity.
• Score: 14.268363583731848
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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