论文标题
Wasserstein Barycenters的随机马鞍点优化
Stochastic Saddle-Point Optimization for Wasserstein Barycenters
论文作者
论文摘要
我们认为，对于有限的点并由在线数据流产生的随机概率措施，我们认为人口瓦斯汀·巴里中心（Wasserstein Barycenter）问题。这导致了一个复杂的随机优化问题，其中将目标作为对函数的期望作为解决随机优化问题的解决方案。我们采用了问题的结构，并获得了对此问题的凸形结合随机鞍点的重新制定。在随机概率度量的分布是离散的情况下，我们提出了一种随机优化算法并估计其复杂性。基于内核方法的第二个结果将前一个扩展到随机概率度量的任意分布。此外，在许多情况下，这种新算法的总复杂性要比随机近似方法和sndhorn算法相结合。我们还通过一系列数值实验来说明我们的发展。
We consider the population Wasserstein barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data. This leads to a complicated stochastic optimization problem where the objective is given as an expectation of a function given as a solution to a random optimization problem. We employ the structure of the problem and obtain a convex-concave stochastic saddle-point reformulation of this problem. In the setting when the distribution of random probability measures is discrete, we propose a stochastic optimization algorithm and estimate its complexity. The second result, based on kernel methods, extends the previous one to the arbitrary distribution of random probability measures. Moreover, this new algorithm has a total complexity better than the Stochastic Approximation approach combined with the Sinkhorn algorithm in many cases. We also illustrate our developments by a series of numerical experiments.
