Reducing Communication in Proximal Newton Methods for Sparse Least Squares Problems

Proximal Newton methods are iterative algorithms that solve l1-regularized least squares problems. Distributed-memory implementation of these methods have become popular since they enable the analysis of large-scale machine learning problems. However, the scalability of these methods is limited by the communication overhead on modern distributed architecture. We propose a stochastic variance-reduced proximal method along with iteration-overlapping and Hessian-reuse to find an efficient trade-off between computation complexity and data communication. The proposed RC-SFSITA algorithm reduces latency costs by a factor of k without altering bandwidth costs. RC-SFISTA is implemented on both MPI and Spark and compared to the state-of-the-art framework, ProxCoCoA. The performance of RC-SFISTA is evaluated on 1 to 512 nodes for multiple benchmarks and demonstrates speedups of up to 12× compared to ProxCoCoA with scaling properties that outperform the original algorithm.