Communication-Efficient Distributed Optimization in Networks with Gradient Tracking and Variance Reduction
This work addresses the communication bottleneck in decentralized optimization for applications like multi-agent and federated learning, offering incremental improvements by adapting master/slave algorithms to network settings.
The paper tackles communication-efficient distributed optimization in decentralized networks by developing Network-DANE, an approximate Newton-type method, and Network-SVRG/SARAH with variance reduction, achieving linear convergence for strongly convex losses and demonstrating improved efficiency in communication and computation over baselines.
There is growing interest in large-scale machine learning and optimization over decentralized networks, e.g. in the context of multi-agent learning and federated learning. Due to the imminent need to alleviate the communication burden, the investigation of communication-efficient distributed optimization algorithms - particularly for empirical risk minimization - has flourished in recent years. A large fraction of these algorithms have been developed for the master/slave setting, relying on a central parameter server that can communicate with all agents. This paper focuses on distributed optimization over networks, or decentralized optimization, where each agent is only allowed to aggregate information from its neighbors. By properly adjusting the global gradient estimate via local averaging in conjunction with proper correction, we develop a communication-efficient approximate Newton-type method Network-DANE, which generalizes DANE to the decentralized scenarios. Our key ideas can be applied in a systematic manner to obtain decentralized versions of other master/slave distributed algorithms. A notable development is Network-SVRG/SARAH, which employs variance reduction to further accelerate local computation. We establish linear convergence of Network-DANE and Network-SVRG for strongly convex losses, and Network-SARAH for quadratic losses, which shed light on the impacts of data homogeneity, network connectivity, and local averaging upon the rate of convergence. We further extend Network-DANE to composite optimization by allowing a nonsmooth penalty term. Numerical evidence is provided to demonstrate the appealing performance of our algorithms over competitive baselines, in terms of both communication and computation efficiency. Our work suggests that performing a certain amount of local communications and computations per iteration can substantially improve the overall efficiency.