A Robust Multi-Batch L-BFGS Method for Machine Learning

TL;DR

This paper introduces a robust multi-batch L-BFGS algorithm tailored for distributed and multi-batch machine learning scenarios, ensuring stability and convergence in the face of asynchronous and changing data evaluations.

Contribution

It proposes a stable quasi-Newton updating scheme for multi-batch settings and analyzes its convergence for convex and nonconvex functions.

Findings

Stable updates improve convergence in distributed environments

Algorithm effectively trains logistic regression and neural networks

Demonstrates robustness against data variability and delays

Abstract

This paper describes an implementation of the L-BFGS method designed to deal with two adversarial situations. The first occurs in distributed computing environments where some of the computational nodes devoted to the evaluation of the function and gradient are unable to return results on time. A similar challenge occurs in a multi-batch approach in which the data points used to compute function and gradients are purposely changed at each iteration to accelerate the learning process. Difficulties arise because L-BFGS employs gradient differences to update the Hessian approximations, and when these gradients are computed using different data points the updating process can be unstable. This paper shows how to perform stable quasi-Newton updating in the multi-batch setting, studies the convergence properties for both convex and nonconvex functions, and illustrates the behavior of the algorithm in a distributed computing platform on binary classification logistic regression and neural network training problems that arise in machine learning.