mL-BFGS: A Momentum-based L-BFGS for Distributed Large-Scale Neural Network Optimization

TL;DR

The paper introduces mL-BFGS, a momentum-enhanced L-BFGS algorithm designed for stable, efficient large-scale distributed neural network training, outperforming traditional optimizers in convergence speed and computational efficiency.

Contribution

mL-BFGS is a novel, lightweight quasi-Newton method that incorporates momentum to stabilize stochastic training and enables distributed large-scale neural network optimization.

Findings

mL-BFGS achieves faster convergence than SGD and Adam.

It provides significant wall-clock speedup in training large neural models.

The method effectively reduces stochastic noise in Hessian approximations.

Abstract

Quasi-Newton methods still face significant challenges in training large-scale neural networks due to additional compute costs in the Hessian related computations and instability issues in stochastic training. A well-known method, L-BFGS that efficiently approximates the Hessian using history parameter and gradient changes, suffers convergence instability in stochastic training. So far, attempts that adapt L-BFGS to large-scale stochastic training incur considerable extra overhead, which offsets its convergence benefits in wall-clock time. In this paper, we propose mL-BFGS, a lightweight momentum-based L-BFGS algorithm that paves the way for quasi-Newton (QN) methods in large-scale distributed deep neural network (DNN) optimization. mL-BFGS introduces a nearly cost-free momentum scheme into L-BFGS update and greatly reduces stochastic noise in the Hessian, therefore stabilizing convergence during stochastic optimization. For model training at a large scale, mL-BFGS approximates a block-wise Hessian, thus enabling distributing compute and memory costs across all computing nodes. We provide a supporting convergence analysis for mL-BFGS in stochastic settings. To investigate mL-BFGS potential in large-scale DNN training, we train benchmark neural models using mL-BFGS and compare performance with baselines (SGD, Adam, and other quasi-Newton methods). Results show that mL-BFGS achieves both noticeable iteration-wise and wall-clock speedup.