Constant Step Size Least-Mean-Square: Bias-Variance Trade-offs and Optimal Sampling Distributions - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2015

Constant Step Size Least-Mean-Square: Bias-Variance Trade-offs and Optimal Sampling Distributions

Abstract

We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide an asymptotic expansion up to explicit exponentially decaying terms. Our analysis leads to new insights into stochastic approximation algorithms: (a) it gives a tighter bound on the allowed step-size; (b) the generalization error may be divided into a variance term which is decaying as O(1/n), independently of the step-size γ, and a bias term that decays as O(1/γ 2 n 2); (c) when allowing non-uniform sampling, the choice of a good sampling density depends on whether the variance or bias terms dominate. In particular, when the variance term dominates, optimal sampling densities do not lead to much gain, while when the bias term dominates, we can choose larger step-sizes that leads to significant improvements.
Fichier principal
Vignette du fichier
paper.pdf (302.63 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01081578 , version 1 (09-11-2014)

Licence

Public Domain

Identifiers

Cite

Alexandre Défossez, Francis Bach. Constant Step Size Least-Mean-Square: Bias-Variance Trade-offs and Optimal Sampling Distributions. International Conference on Artificial Intelligence and Statistics (AISTATS),, 2015, San Diego, United States. ⟨hal-01081578⟩
209 View
168 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More