The Nesterov-Spokoiny Acceleration Achieves Strict $o(1/k^2)$ Convergence
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911259902869504 |
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| author | Peng, Weibin Liu, Yu Wang, Tianyu |
| author_facet | Peng, Weibin Liu, Yu Wang, Tianyu |
| contents | This paper studies the Nesterov-Spokoiny Acceleration (NSA), a variant of the accelerated gradient method by Nesterov and Spokoiny. For smooth convex optimization, NSA achieves a strict $o(1/k^2)$ convergence rate in function value and an $o(1/(k^3 \log k))$ rate in squared gradient norm, while ensuring monotonic descent of the objective. We further study a zeroth-order version of NSA that handles inexact gradients, and extends NSA to composite optimization problems, in each case establishing $o(1/k^2)$ convergence in function value. A continuous-time analysis reveals connections to high-resolution ODEs known to underlie acceleration phenomena. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_14314 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Nesterov-Spokoiny Acceleration Achieves Strict $o(1/k^2)$ Convergence Peng, Weibin Liu, Yu Wang, Tianyu Optimization and Control This paper studies the Nesterov-Spokoiny Acceleration (NSA), a variant of the accelerated gradient method by Nesterov and Spokoiny. For smooth convex optimization, NSA achieves a strict $o(1/k^2)$ convergence rate in function value and an $o(1/(k^3 \log k))$ rate in squared gradient norm, while ensuring monotonic descent of the objective. We further study a zeroth-order version of NSA that handles inexact gradients, and extends NSA to composite optimization problems, in each case establishing $o(1/k^2)$ convergence in function value. A continuous-time analysis reveals connections to high-resolution ODEs known to underlie acceleration phenomena. |
| title | The Nesterov-Spokoiny Acceleration Achieves Strict $o(1/k^2)$ Convergence |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2308.14314 |