Time-independent Generalization Bounds for SGLD in Non-convex Settings

Tyler Farghly; Patrick Rebeschini

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arXiv · 2111.12876

Time-independent Generalization Bounds for SGLD in Non-convex Settings

Tyler Farghly·Patrick Rebeschini

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Abstract

We establish generalization error bounds for stochastic gradient Langevin dynamics (SGLD) with constant learning rate under the assumptions of dissipativity and smoothness, a setting that has received increased attention in the sampling/optimization literature. Unlike existing bounds for SGLD in non-convex settings, ours are time-independent and decay to zero as the sample size increases. Using the framework of uniform stability, we establish time-independent bounds by exploiting the Wasserstein contraction property of the Langevin diffusion, which also allows us to circumvent the need to bound gradients using Lipschitz-like assumptions. Our analysis also supports variants of SGLD that use different discretization methods, incorporate Euclidean projections, or use non-isotropic noise.

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stat.ML cs.LG math.OC math.PR

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BibTeX RIS

Tyler Farghly, Patrick Rebeschini. 2021-11-25. Time-independent Generalization Bounds for SGLD in Non-convex Settings. https://arxiv.org/abs/2111.12876

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