Asymptotic Time-Uniform Inference for Parameters in Averaged Stochastic Approximation

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Xie, Chuhan, Jin, Kaicheng, Liang, Jiadong, Zhang, Zhihua
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866914980453941248
author Xie, Chuhan
Jin, Kaicheng
Liang, Jiadong
Zhang, Zhihua
author_facet Xie, Chuhan
Jin, Kaicheng
Liang, Jiadong
Zhang, Zhihua
contents We study time-uniform statistical inference for parameters in stochastic approximation (SA), which encompasses a bunch of applications in optimization and machine learning. To that end, we analyze the almost-sure convergence rates of the averaged iterates to a scaled sum of Gaussians in both linear and nonlinear SA problems. We then construct three types of asymptotic confidence sequences that are valid uniformly across all times with coverage guarantees, in an asymptotic sense that the starting time is sufficiently large. These coverage guarantees remain valid if the unknown covariance matrix is replaced by its plug-in estimator, and we conduct experiments to validate our methodology.
format Preprint
id arxiv_https___arxiv_org_abs_2410_15057
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Asymptotic Time-Uniform Inference for Parameters in Averaged Stochastic Approximation
Xie, Chuhan
Jin, Kaicheng
Liang, Jiadong
Zhang, Zhihua
Machine Learning
Methodology
We study time-uniform statistical inference for parameters in stochastic approximation (SA), which encompasses a bunch of applications in optimization and machine learning. To that end, we analyze the almost-sure convergence rates of the averaged iterates to a scaled sum of Gaussians in both linear and nonlinear SA problems. We then construct three types of asymptotic confidence sequences that are valid uniformly across all times with coverage guarantees, in an asymptotic sense that the starting time is sufficiently large. These coverage guarantees remain valid if the unknown covariance matrix is replaced by its plug-in estimator, and we conduct experiments to validate our methodology.
title Asymptotic Time-Uniform Inference for Parameters in Averaged Stochastic Approximation
topic Machine Learning
Methodology
url https://arxiv.org/abs/2410.15057