On the rates of convergence of parallelized averaged stochastic gradient algorithms. Issue 3 (3rd May 2020)

• Record Type: Journal Article
• Authors: Godichon-Baggioni, Antoine; Saadane, Sofiane
• Is Part Of: Statistics. Volume 54:Issue 3(2020)
• Page Start: 618
• Page End: 635
• Publication Date: 2020-05-03
• Subjects: Stochastic gradient descent -- averaging -- distributed estimation -- central limit theorem -- asynchronous parallel optimization; 62L20 -- 62H12; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2020.1764557
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: The growing interest for high-dimensional and functional data analysis led in the last decade to important research developing a consequent amount of techniques. Parallelized algorithms, which consist of distributing and treat the data into different machines, for example, are a good answer to deal with large samples taking values in high-dimensional spaces. We introduce here a parallelized averaged stochastic gradient algorithm, which enables to treat efficiently and recursively the data, and so, without taking care if the distribution of the data into the machines is uniform. The rate of convergence in quadratic mean, as well as the asymptotic normality of the parallelized estimates are given, for strongly and locally strongly convex objectives.