Distributed Algorithms with Variance Reduction for Calculating Wasserstein Barycenters

Student: Arzhantsev Andrei

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Final Grade: 8

Year of Graduation: 2024

This work is focused on Wasserstein barycenters (WB) problem, which is an important application of optimal transport (OT) problem. WB can be considered as a saddle point optimization problem, for which many methods are developed and studied. Recent articles related to this topic had improvements in complexity bounds for the problem, obtained through the use of optimization methods such as MirrorProx or Dual extrapolation. Other studies in the field of saddle point optimization problems demonstrate that algorithms can be improved due to the proper utilization of variance reduction techniques. Investigation of the non-Euclidean setup of WB problem and generalization of the newest algorithms for it is the main goal of the work. Comparison with existing methods is considered as well.

Full text (added May 20, 2024)

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