March 15, 2025
Accelerating optimization over the space of probability measures
Accelerating optimization over the space of probability measures Shi Chen, Qin Li, Oliver Tse, Stephen J. Wright; 26(31):1−40, 2025. Abstract The acceleration of gradient-based optimization methods is a subject of significant practical and theoretical importance, particularly within machine learning applications. While much attention has been directed towards optimizing within Euclidean space, the need to optimize over spaces of probability measures in machine learning motivates the exploration of accelerated gradient methods in this context, too. To this end, we introduce a Hamiltonian-flow approach analogous to momentum-based approaches in Euclidean space. We demonstrate that, in the continuous-time setting, algorithms based on this