On the Convergence of Nesterov’s Accelerated Gradient Method in Stochastic Settings

August 14, 2020


We study Nesterov’s accelerated gradient method with constant step-size and momentum parameters in the stochastic approximation setting (unbiased gradients with bounded variance) and the finite-sum setting (where randomness is due to sampling mini-batches). To build better insight into the behavior of Nesterov’s method in stochastic settings, we focus throughout on objectives that are smooth, strongly-convex, and twice continuously differentiable. In the stochastic approximation setting, Nesterov’s method converges to a neighborhood of the optimal point at the same accelerated rate as in the deterministic setting. Perhaps surprisingly, in the finite-sum setting, we prove that Nesterov’s method may diverge with the usual choice of step-size and momentum, unless additional conditions on the problem related to conditioning and data coherence are satisfied. Our results shed light as to why Nesterov’s method may fail to converge or achieve acceleration in the finite-sum setting.

Download the Paper


Written by

Mido Assran

Michael Rabbat


International Conference on Machine Learning (ICML)

Research Topics

Machine Learning

Related Publications

June 02, 2019

Simple Attention-Based Representation Learning for Ranking Short Social Media Posts | Facebook AI Research

This paper explores the problem of ranking short social media posts with respect to user queries using neural networks. Instead of starting with a complex architecture, we proceed from the bottom up and examine the effectiveness of a simple,…

Peng Shi, Jinfeng Rao, Jimmy Lin

June 02, 2019

June 09, 2019


First-order Adversarial Vulnerability of Neural Networks and Input Dimension | Facebook AI Research

Over the past few years, neural networks were proven vulnerable to adversarial images: targeted but imperceptible image perturbations lead to drastically different predictions. We show that adversarial vulnerability increases with the gradients…

Carl-Johann Simon-Gabriel, Yann Ollivier, Bernhard Scholkopf, Leon Bottou, David Lopez-Paz

June 09, 2019

May 31, 2019


Abusive Language Detection with Graph Convolutional Networks | Facebook AI Research

Abuse on the Internet represents a significant societal problem of our time. Previous research on automated abusive language detection in Twitter has shown that community-based profiling of users is a promising technique for this task. However,…

Pushkar Mishra, Marco Del Tredici, Helen Yannakoudakis, Ekaterina Shutova

May 31, 2019

June 01, 2019

Probabilistic Planning with Reduced Models | Facebook AI Research

Reduced models are simplified versions of a given domain, designed to accelerate the planning process. Interest in reduced models has grown since the surprising success of determinization in the first international probabilistic planning…

Luis Pineda, Shlomo Zilberstein

June 01, 2019

Help Us Pioneer The Future of AI

We share our open source frameworks, tools, libraries, and models for everything from research exploration to large-scale production deployment.