When Momentum Helps Polyak--Ruppert Averaging
Polyak--Ruppert averaging gives SGD and momentum methods the same asymptotic covariance. We characterize how fast finite runs reach it and how far they can be parallelized. For strongly convex quadratics with additive noise, we prove an online--offline bridge: the empirical risk minimizer on the samples of a tail average is one Newton step from the tail-averaged query point of any online procedure. For SGD, heavy ball, and Nesterov's method with constant momentum, this step is a boundary term at the two ends of the tail and splits the gap to the offline estimator into center, covariance, and shape errors. Necessary and sufficient conditions show that, on the least curved direction, the ce...
| Authors | Alexandra Suvroikova, Darina Dvinskikh, Yuriy Dorn et al. |
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| Primary category | cs.LG |
| Published | 20 October 2026 |
| Last updated at source | 20 October 2026 |
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