A Multi-Batch L-BFGS Method for Machine Learning

TL;DR

This paper introduces a multi-batch L-BFGS method that enables stable second-order optimization in distributed machine learning by changing data batches at each iteration, improving convergence for convex and nonconvex problems.

Contribution

It proposes a novel stable quasi-Newton updating scheme for multi-batch L-BFGS, addressing instability issues in distributed second-order optimization.

Findings

Demonstrates stable convergence in distributed settings

Shows effectiveness for convex and nonconvex problems

Analyzes algorithm behavior in parallel computing environments

Abstract

The question of how to parallelize the stochastic gradient descent (SGD) method has received much attention in the literature. In this paper, we focus instead on batch methods that use a sizeable fraction of the training set at each iteration to facilitate parallelism, and that employ second-order information. In order to improve the learning process, we follow a multi-batch approach in which the batch changes at each iteration. This can cause difficulties because L-BFGS employs gradient differences to update the Hessian approximations, and when these gradients are computed using different data points the process can be unstable. This paper shows how to perform stable quasi-Newton updating in the multi-batch setting, illustrates the behavior of the algorithm in a distributed computing platform, and studies its convergence properties for both the convex and nonconvex cases.