  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.
