S-NEAR-DGD：一种灵活的分布式随机梯度法
S-NEAR-DGD: A Flexible Distributed Stochastic Gradient Method for Inexact Communication
摘要：
我们提出并分析了一种随机分布式方法（S-NEAR-DGD），它可以容忍不精确的计算和不准确的信息交换，以减轻大规模系统中昂贵的梯度评估和带宽有限的通信问题。我们的方法是基于一类灵活的，分布式的一阶算法，允许计算和通信的权衡，以最好地适应应用程序的设置。我们假设节点之间的所有信息交换都受到随机失真的影响，并且只有真实梯度的随机逼近可用。我们的理论结果证明了所提出的算法在期望线性收敛到最优解的一个邻域的强凸目标函数与Lipschitz梯度。我们的特征依赖于算法和网络参数，通信信道的质量和所使用的随机梯度近似的精度，这附近。最后，我们提供了数值结果来评估我们的方法的经验性能。
英文摘要：
We present and analyze a stochastic distributed method (S-NEAR-DGD) that can tolerate inexact computation and inaccurate information exchange to alleviate the problems of costly gradient evaluations and bandwidth-limited communication in large-scale systems. Our method is based on a class of flexible, distributed first order algorithms that allow for the trade-off of computation and communication to best accommodate the application setting. We assume that all the information exchange between nodes is subject to random distortion and that only stochastic approximations of the true gradients are available. Our theoretical results prove that the proposed algorithm converges linearly in expectation to a neighborhood of the optimal solution for strongly convex objective functions with Lipschitz gradients. We characterize the dependence of this neighborhood on algorithm and network parameters, the quality of the communication channel and the precision of the stochastic gradient approximations used. Finally, we provide numerical results to evaluate the empirical performance of our method.
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