Mathematics > Optimization and Control
[Submitted on 14 Jun 2020 (v1), last revised 9 Dec 2020 (this version, v2)]
Title:Wasserstein barycenters can be computed in polynomial time in fixed dimension
View PDFAbstract:Computing Wasserstein barycenters is a fundamental geometric problem with widespread applications in machine learning, statistics, and computer graphics. However, it is unknown whether Wasserstein barycenters can be computed in polynomial time, either exactly or to high precision (i.e., with $\textrm{polylog}(1/\varepsilon)$ runtime dependence). This paper answers these questions in the affirmative for any fixed dimension. Our approach is to solve an exponential-size linear programming formulation by efficiently implementing the corresponding separation oracle using techniques from computational geometry.
Submission history
From: Jason Altschuler [view email][v1] Sun, 14 Jun 2020 20:24:27 UTC (248 KB)
[v2] Wed, 9 Dec 2020 22:15:32 UTC (1,734 KB)
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