Stochastic optimization under time drift: iterate averaging, step-decay schedules, and high probability guarantees
Datasets and Benchmarks Track
Authors: Joshua Cutler, Dmitriy Drusvyatskiy, Zaid Harchaoui

We consider the problem of minimizing a convex function that is evolving in time according to unknown and possibly stochastic dynamics. Such problems abound in the machine learning and signal processing literature, under the names of concept drift and stochastic tracking. We provide novel non-asymptotic convergence guarantees for stochastic algorithms with iterate averaging, focusing on bounds valid both in expectation and with high probability. Notably, we show that the tracking efficiency of the proximal stochastic gradient method depends only logarithmically on the initialization quality when equipped with a step-decay schedule.