GIANT: Globally Improved Approximate Newton Method for Distributed Optimization

TL;DR

GIANT is a communication-efficient distributed optimization method that combines local approximate Newton steps with a global averaging scheme, achieving faster convergence with minimal tuning.

Contribution

This paper introduces GIANT, a novel distributed Newton-type method that improves convergence rates and reduces communication costs with only one tuning parameter.

Findings

GIANT outperforms existing methods in convergence speed.

It requires fewer communication rounds in distributed settings.

Empirical results show superior performance on large-scale problems.

Abstract

For distributed computing environment, we consider the empirical risk minimization problem and propose a distributed and communication-efficient Newton-type optimization method. At every iteration, each worker locally finds an Approximate NewTon (ANT) direction, which is sent to the main driver. The main driver, then, averages all the ANT directions received from workers to form a {\it Globally Improved ANT} (GIANT) direction. GIANT is highly communication efficient and naturally exploits the trade-offs between local computations and global communications in that more local computations result in fewer overall rounds of communications. Theoretically, we show that GIANT enjoys an improved convergence rate as compared with first-order methods and existing distributed Newton-type methods. Further, and in sharp contrast with many existing distributed Newton-type methods, as well as popular first-order methods, a highly advantageous practical feature of GIANT is that it only involves one tuning parameter. We conduct large-scale experiments on a computer cluster and, empirically, demonstrate the superior performance of GIANT.