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

Tyler Farghly, Patrick Rebeschini

Keywords: SGLD, Langevin, stochastic gradient, generalization, stability, non-convex, wasserstein, optimization

TL;DR: In the setting of non-convex learning, we derive generalization error bounds for SGLD that are time-independent and decay to zero as the sample size increases

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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