Asymptotic Time-Uniform Inference for Parameters in Averaged Stochastic Approximation
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| 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 |