Federated calculation of the free-support transportation barycenter by single-loop dual decomposition
提出一种高效的联邦对偶分解算法，用于计算多个分布的Wasserstein重心，包括选择解的支撑集。算法不访问本地数据，仅使用高度聚合信息，且无需重复求解运输问题，每次迭代复杂度低，具有良好的可扩展性。
Abstract We propose an efficient federated dual decomposition algorithm for calculating the Wasserstein barycenter of several distributions, including choosing the support of the solution. The algorithm does not access local data and uses only highly aggregated information. It also does not require repeated solutions to mass transportation problems. Because of the absence of any matrix–vector operations, the algorithm exhibits a very low complexity of each iteration and significant scalability. We illustrate its virtues and compare it to the state-of-the-art methods on several examples of mixture models.