论文标题
随着时间变化的网络的分散式凸优化，并应用于Wasserstein Barycenters
Decentralized Convex Optimization on Time-Varying Networks with Application to Wasserstein Barycenters
论文作者
论文摘要
受到近似临近瓦斯坦·巴里焦的分布式算法的最新进展的启发，我们为此问题提出了一种新颖的分布算法。主要的新颖性是我们考虑时变计算网络，这些计算网络是由只有一部分传感器可以在每个时间步骤进行观察的示例的动机，但是，目的是通过近似于其Barycenter来平均信号（例如某些区域的卫星图片）。我们将这个问题嵌入到一类不平滑的双重友好分布式优化问题上，并在时间变化的网络上为此类别开发一阶方法。我们证明，从Nesterov收敛速率的意义上提出了非反应加速，并明确表征了它们对网络参数及其动力学的依赖。在实验中，当应用于Wasserstein Barycenter问题时，我们证明了所提出的算法的效率。
Inspired by recent advances in distributed algorithms for approximating Wasserstein barycenters, we propose a novel distributed algorithm for this problem. The main novelty is that we consider time-varying computational networks, which are motivated by examples when only a subset of sensors can make an observation at each time step, and yet, the goal is to average signals (e.g., satellite pictures of some area) by approximating their barycenter. We embed this problem into a class of non-smooth dual-friendly distributed optimization problems over time-varying networks, and develop a first-order method for this class. We prove non-asymptotic accelerated in the sense of Nesterov convergence rates and explicitly characterise their dependence on the parameters of the network and its dynamics. In the experiments, we demonstrate the efficiency of the proposed algorithm when applied to the Wasserstein barycenter problem.
