Quasi-Newton updating for large-scale distributed learning

Shuyuan Wu, Danyang Huang, Hansheng Wang

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2023 · Volume 85 · Issue 4

Abstract

Distributed computing is critically important for modern statistical analysis. Herein, we develop a distributed quasi-Newton (DQN) framework with excellent statistical, computation, and communication efficiency. In the DQN method, no Hessian matrix inversion or communication is needed. This considerably reduces the computation and communication complexity of the proposed method. Notably, related existing methods only analyse numerical convergence and require a diverging number of iterations to converge. However, we investigate the statistical properties of the DQN method and theoretically demonstrate that the resulting estimator is statistically efficient over a small number of iterations under mild conditions. Extensive numerical analyses demonstrate the finite sample performance.

Keywords

communication efficiency, computation efficiency, distributed system, quasi-Newton methods, statistical efficiency

Enable JavaScript for citation tools and additional paper interactions.