Stopping Rules for Stochastic Gradient Descent via Anytime-Valid Confidence Sequences
Abstract
We study a basic but unresolved question in stochastic optimization: when should stochastic gradient descent (SGD) be stopped based only on its observed trajectory? We develop anytime-valid confidence sequences for stochastic gradient methods that remain valid under continuous monitoring and directly yield statistically valid stopping rules. In convex optimization, they certify weighted suboptimality under general stepsize schedules; in nonconvex optimization, they certify weighted first-order stationarity. The result is a unified framework for online stopping of SGD with provable complexity guarantees.
Bio
Liviu Aolaritei is a postdoctoral researcher in EECS at UC Berkeley, hosted by Michael I. Jordan. Previously, he completed his PhD in the Automatic Control Laboratory at ETH Zurich under the supervision of Florian Dörfler. His research lies at the intersection of optimization, statistics, and computation, focusing on decision-making under complex uncertainty such as distribution shifts, rare events, and graph-structured uncertainty.