This work proposes a distributed algorithm for solving empirical risk minimization problems, called L-DQN, under the master/worker communication model. L-DQN is a distributed limited-memory quasi-Newton method that supports asynchronous computations among the worker nodes. Our method is efficient both in terms of storage and communication costs, i.e., in every iteration the master node and workers communicate vectors of size $O(d)$, where $d$ is the dimension of the decision variable, and the amount of memory required on each node is $O(md)$, where $m$ is an adjustable parameter. To our knowledge, this is the first distributed quasi-Newton method with provable global linear convergence guarantees in the asynchronous setting where delays between nodes are present. Numerical experiments are provided to illustrate the theory and the practical performance of our method.

翻译：这项工作提出了一种分散算法,用于在主机/工人通信模式下解决尽量减少风险的经验问题,称为L-DQN。L-DQN是一种分布式的有限模数准牛顿方法,支持工人节点之间的非同步计算。我们的方法在储存和通信成本方面都是有效的,即在每次迭代中,主节点和工人沟通大小为O(d)美元的矢量,其中决定变量的维度为$(d)美元,每个节点所需的内存量为$(md)美元,其中美元是一个可调整的参数。据我们了解,这是第一种分布式准牛顿方法,在节点之间出现延误的无序设置中具有可辨别的全球线性趋同保证。提供了数字实验,以说明我们方法的理论和实际性能。