A Parameter-Free Restart Scheme with Only a Parallelizable $\log\log(1/ε)$ Overhead
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918530388066304 |
|---|---|
| author | Wu, Yue Grimmer, Benjamin |
| author_facet | Wu, Yue Grimmer, Benjamin |
| contents | It is well-known that first-order methods can offer accelerated convergence rates in the presence of growth structures. Restarting schemes provide a general tool for such speed-ups. These schemes typically either require unrealistic problem knowledge, incur logarithmic overhead factors in oracle complexity, and/or have a nontrivial initial burn-in phase. We present a parameter-free approach for restarting any first-order method, avoiding these three drawbacks. Our approach dynamically deploys parallel instances of a given first-order method communicating progress in the style of Renegar and Grimmer. Our optimized scheme avoids expensive burn-ins and only requires $O(\log\log(1/ε))$ parallel processes when the accelerated rate is sublinear. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30502 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Parameter-Free Restart Scheme with Only a Parallelizable $\log\log(1/ε)$ Overhead Wu, Yue Grimmer, Benjamin Optimization and Control It is well-known that first-order methods can offer accelerated convergence rates in the presence of growth structures. Restarting schemes provide a general tool for such speed-ups. These schemes typically either require unrealistic problem knowledge, incur logarithmic overhead factors in oracle complexity, and/or have a nontrivial initial burn-in phase. We present a parameter-free approach for restarting any first-order method, avoiding these three drawbacks. Our approach dynamically deploys parallel instances of a given first-order method communicating progress in the style of Renegar and Grimmer. Our optimized scheme avoids expensive burn-ins and only requires $O(\log\log(1/ε))$ parallel processes when the accelerated rate is sublinear. |
| title | A Parameter-Free Restart Scheme with Only a Parallelizable $\log\log(1/ε)$ Overhead |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.30502 |