Scaling Limits of Constant-Stepsize SGD at Flat Minima
For stochastic gradient descent (SGD) with a constant stepsize $α$, the invariant law of the iterates, centered at a minimizer, describes the behavior of the algorithm over long time horizons. In the strongly convex case, this invariant law has the familiar $\sqrtα$ scaling and a Gaussian limit as $α\downarrow 0$. We show that this behavior changes fundamentally for convex objectives $H$ with flat minima and (sub)quadratic tails. More specifically, we study SGD with Markovian noise generated by a contractive driving chain. For every sufficiently small constant stepsize $α$, we prove existence, uniqueness, and geometric convergence to an augmented invariant law in a Wasserstein distance in...
| Authors | Jingyi Zhang, Cheng Mao, Debankur Mukherjee |
|---|---|
| Primary category | cs.LG |
| Published | 17 July 2026 |
| Last updated at source | 17 July 2026 |
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