The Nesterov-Spokoiny Acceleration Achieves Strict $o(1/k^2)$ Convergence

Weibin Peng; Yu Liu; Tianyu Wang

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arXiv · 2308.14314

The Nesterov-Spokoiny Acceleration Achieves Strict $o(1/k^2)$ Convergence

Weibin Peng·Yu Liu·Tianyu Wang

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Abstract

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.

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BibTeX RIS

Weibin Peng, Yu Liu, Tianyu Wang. 2023-08-28. The Nesterov-Spokoiny Acceleration Achieves Strict $o(1/k^2)$ Convergence. https://arxiv.org/abs/2308.14314

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