Last Iterate Convergence of Incremental Methods and Applications in Continual Learning

arXiv:2403.06873v1 Announce Type: cross
Abstract: Incremental gradient methods and incremental proximal methods are a fundamental class of optimization algorithms used for solving finite sum problems, broadly studied in the literature. Yet, when it comes to their convergence guarantees, nonasymptotic (first-order or proximal) oracle complexity bounds have been obtained fairly recently, almost exclusively applying to the average iterate. Motivated by applications in continual learning, we obtain the first convergence guarantees for the last iterate of both incremental gradient and incremental proximal …

abstract algorithms applications arxiv class complexity continual convergence cs.lg gradient incremental iterate literature math.oc optimization oracle type