Sharp Stationary Gaussian Approximation for Constant-Stepsize SGD

Excerpt

arXiv:2609.39144v1 Announce Type: new Abstract: We prove a sharp Gaussian approximation for the invariant law of constant-stepsize SGD with bounded additive noise generated by an exogenous uniformly ergodic Markov chain. For a smooth, strongly convex objective with a Lipschitz Hessian and nondegenerate long-run noise covariance, the centered iterate normalized by the square root of the stepsize is $O(\sqrt{\alpha})$-close in 1-Wasserstein distance to its limiting Gaussian. The proof combines blo