Paper
Stopping Rules for Stochastic Gradient Descent via Anytime-Valid Confidence Sequences
Authors
Liviu Aolaritei, Michael I. Jordan
Abstract
We study stopping rules for stochastic gradient descent (SGD) for convex optimization from the perspective of anytime-valid confidence sequences. Classical analyses of SGD provide convergence guarantees in expectation or at a fixed horizon, but offer no statistically valid way to assess, at an arbitrary time, how close the current iterate is to the optimum. We develop an anytime-valid, data-dependent upper confidence sequence for the weighted average suboptimality of projected SGD, constructed via nonnegative supermartingales and requiring no smoothness or strong convexity. This confidence sequence yields a simple stopping rule that is provably -optimal with probability at least and is almost surely finite under standard stochastic approximation stepsizes. To the best of our knowledge, these are the first rigorous, time-uniform performance guarantees and finite-time -optimality certificates for projected SGD with general convex objectives, based solely on observable trajectory quantities.