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- W4313304931 abstract "To date, no information-theoretic frameworks for reasoning about generalization error have been shown to establish minimax rates for gradient descent in the setting of stochastic convex optimization. In this work, we consider the prospect of establishing such rates via several existing information-theoretic frameworks: input-output mutual information bounds, conditional mutual information bounds and variants, PAC-Bayes bounds, and recent conditional variants thereof. We prove that none of these bounds are able to establish minimax rates. We then consider a common tactic employed in studying gradient methods, whereby the final iterate is corrupted by Gaussian noise, producing a noisy surrogate algorithm. We prove that minimax rates cannot be established via the analysis of such surrogates. Our results suggest that new ideas are required to analyze gradient descent using information-theoretic techniques." @default.
- W4313304931 created "2023-01-06" @default.
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- W4313304931 date "2022-12-27" @default.
- W4313304931 modified "2023-09-23" @default.
- W4313304931 title "Limitations of Information-Theoretic Generalization Bounds for Gradient Descent Methods in Stochastic Convex Optimization" @default.
- W4313304931 doi "https://doi.org/10.48550/arxiv.2212.13556" @default.
- W4313304931 hasPublicationYear "2022" @default.
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