Papers › The Nesterov-Spokoiny Acceleration Achieves Strict o(1/k²) Convergence
The Nesterov-Spokoiny Acceleration Achieves Strict o(1/k²) Convergence
Weibin Peng, Yu Liu, Tianyu Wang
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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/k²) convergence rate in function value and an o(1/(k³ logk)) 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/k²) convergence in function value. A continuous-time analysis reveals connections to high-resolution ODEs known to underlie acceleration phenomena.
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