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In this paper, we focus on computational aspects of the Wassersteinbarycenter problem. We propose two algorithms to compute Wassersteinbarycenters of $m$ discrete measures of size $n$ with accuracy $\e$. The firstalgorithm, based on mirror prox with a specific norm, meets the complexity ofcelebrated accelerated iterative Bregman projections (IBP), namely $\widetildeO(mn^2\sqrt n/\e)$, however, with no limitations in contrast to the(accelerated) IBP, which is numerically unstable under small regularizationparameter. The second algorithm, based on area-convexity and dualextrapolation, improves the previously best-known convergence rates for theWasserstein barycenter problem enjoying $\widetilde O(mn^2/\e)$ complexity.

Improved Complexity Bounds in Wasserstein Barycenter Problem