Acceleration via silver step-size on Riemannian manifolds with applications to Wasserstein space
Abstract
There is extensive literature on accelerating first-order optimization methods in a Euclidean setting. Under which conditions such acceleration is feasible in Riemannian optimization problems is an active area of research. Motivated by the recent success of dynamic stepsize methods in the Euclidean setting, we undertake a study of such algorithms in the Riemannian setting. We provide the new class of algorithms determined by the choice of vector transport that allows the dynamic stepsize acceleration on Riemannian manifolds for the function classes associated with the corresponding vector transport. As a core application, we show our algorithm recovers the standard Wasserstein gradient descent on 2-Wasserstein space, and as a result provides the first provable accelerated gradient method in Wasserstein space. In addition, we validate the numerical strength of the algorithm for standard benchmark tasks on the space of symmetric positive definite matrices.
Cite
@article{arxiv.2506.06160,
title = {Acceleration via silver step-size on Riemannian manifolds with applications to Wasserstein space},
author = {Jiyoung Park and Abhishek Roy and Jonathan W. Siegel and Anirban Bhattacharya},
journal= {arXiv preprint arXiv:2506.06160},
year = {2025}
}
Comments
We identified an algebraic error in our previous analysis, which invalidated the original results. To correct this, we have revised the algorithm and updated the analysis accordingly