Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimization
This work provides a more efficient and unbiased method for computing Wasserstein-2 barycenters, which is important for researchers and practitioners working with optimal transport and averaging probability measures.
This paper introduces a scalable algorithm for estimating continuous Wasserstein-2 barycenters from sample access to input measures. It achieves this by using input convex neural networks and cycle-consistency regularization, avoiding the minimax optimization typically associated with entropic or quadratic regularization methods.
Wasserstein barycenters provide a geometric notion of the weighted average of probability measures based on optimal transport. In this paper, we present a scalable algorithm to compute Wasserstein-2 barycenters given sample access to the input measures, which are not restricted to being discrete. While past approaches rely on entropic or quadratic regularization, we employ input convex neural networks and cycle-consistency regularization to avoid introducing bias. As a result, our approach does not resort to minimax optimization. We provide theoretical analysis on error bounds as well as empirical evidence of the effectiveness of the proposed approach in low-dimensional qualitative scenarios and high-dimensional quantitative experiments.