Randomized Momentum Transport with Cheap Predictors

Abstract:Momentum methods such as STORM and second-order momentum track the gradient by adding a transport correction to momentum, at the cost of an extra oracle call per iteration. We introduce randomized momentum transport, which evaluates the correction with probability $q$ and otherwise uses a cheap prediction, with importance weighting that preserves the conditional mean and adds $(q^{-1}-1)$ times the prediction loss to the variance. Under transport-bias, second-moment, and residual-control assumptions, linear minimization oracle (LMO) updates, including normalized, sign, and exact spectral (Muon) directions, retain an $O(T^{-1/3})$ stationarity bound for each fixed $q>0$ with a single-gradient initialization. For unnormalized STORM, some $q<1$ lowers the leading coefficient of our sufficient gradient budget if and only if the gradient-difference noise modulus exceeds the smoothness constant, by at most about $10\%$. An online diagonal predictor admits a regret-to-convergence guarantee. At approximately equal oracle cost, querying a quarter of the corrections lowers the final training loss by $18$ to $43\%$ on MNIST1D and raises the test accuracy of Hessian-vector transport on CIFAR-10 by $1.5$ points.

Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2610.13789 [cs.LG]

(or arXiv:2610.13789v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.13789 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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