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Information-Theoretic Generalization Bounds for SGLD via Data-Dependent Estimates
Jeffrey Negrea · Mahdi Haghifam · Gintare Karolina Dziugaite · Ashish Khisti · Daniel Roy

Thu Dec 12 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #232

In this work, we improve upon the stepwise analysis of noisy iterative learning algorithms initiated by Pensia, Jog, and Loh (2018) and recently extended by Bu, Zou, and Veeravalli (2019). Our main contributions are significantly improved mutual information bounds for Stochastic Gradient Langevin Dynamics via data-dependent estimates. Our approach is based on the variational characterization of mutual information and the use of data-dependent priors that forecast the mini-batch gradient based on a subset of the training samples. Our approach is broadly applicable within the information-theoretic framework of Russo and Zou (2015) and Xu and Raginsky (2017). Our bound can be tied to a measure of flatness of the empirical risk surface. As compared with other bounds that depend on the squared norms of gradients, empirical investigations show that the terms in our bounds are orders of magnitude smaller.

Author Information

Jeffrey Negrea (University of Toronto)
Mahdi Haghifam (University of Toronto)
Gintare Karolina Dziugaite (Element AI)
Ashish Khisti (University of Toronto)
Dan Roy (Univ of Toronto & Vector)

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