Select without Fear: Almost All Mini-Batch Schedules Generalize Optimally

Autor:	Nikolakakis, Konstantinos E., Karbasi, Amin, Kalogerias, Dionysis
Rok vydání:	2023
Předmět:	Computer Science - Machine Learning Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	We establish matching upper and lower generalization error bounds for mini-batch Gradient Descent (GD) training with either deterministic or stochastic, data-independent, but otherwise arbitrary batch selection rules. We consider smooth Lipschitz-convex/nonconvex/strongly-convex loss functions, and show that classical upper bounds for Stochastic GD (SGD) also hold verbatim for such arbitrary nonadaptive batch schedules, including all deterministic ones. Further, for convex and strongly-convex losses we prove matching lower bounds directly on the generalization error uniform over the aforementioned class of batch schedules, showing that all such batch schedules generalize optimally. Lastly, for smooth (non-Lipschitz) nonconvex losses, we show that full-batch (deterministic) GD is essentially optimal, among all possible batch schedules within the considered class, including all stochastic ones. Comment: 37 pages, 2 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.02247 Zobrazit plný text záznamu View this record from Arxiv