Provable Accelerated Convergence of Nesterov's Momentum for Deep ReLU Neural Networks

Autor:	Liao, Fangshuo, Kyrillidis, Anastasios
Rok vydání:	2023
Předmět:	Computer Science - Machine Learning Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	Current state-of-the-art analyses on the convergence of gradient descent for training neural networks focus on characterizing properties of the loss landscape, such as the Polyak-Lojaciewicz (PL) condition and the restricted strong convexity. While gradient descent converges linearly under such conditions, it remains an open question whether Nesterov's momentum enjoys accelerated convergence under similar settings and assumptions. In this work, we consider a new class of objective functions, where only a subset of the parameters satisfies strong convexity, and show Nesterov's momentum achieves acceleration in theory for this objective class. We provide two realizations of the problem class, one of which is deep ReLU networks, which --to the best of our knowledge--constitutes this work the first that proves accelerated convergence rate for non-trivial neural network architectures. Comment: Accepted by ALT 2024
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.08109 Zobrazit plný text záznamu View this record from Arxiv