Paper Proves No Gradient Descent Stepsize Schedule Can Match Nesterov Acceleration

prof_grimmer · x · 2026-08-12

A new paper by Jianhao Ma and Yuxin Chen, with parts of the proof developed by GPT, answers a long-standing question in optimization theory.

The authors rigorously prove that no gradient descent stepsize schedule (fractally or otherwise) can achieve full acceleration, meaning it cannot match the theoretical limits of Nesterov's accelerated gradient method.

Combined with a previous lower bound of p=1.2716, this new result establishes an impossibility upper bound of p>1.9319, further narrowing the gap in understanding the theoretical limits of optimization algorithms.

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