An Adaptive Memory Multi-Batch L-BFGS Algorithm for Neural Network Training

TL;DR

This paper introduces MB-AM, an adaptive multi-batch L-BFGS algorithm that gradually increases trust in curvature information, leading to faster convergence and better solutions in neural network training.

Contribution

It proposes a novel development-based scheme to adaptively control second order information use in multi-batch L-BFGS for neural networks.

Findings

MB-AM converges slightly faster than standard multi-batch L-BFGS.

MB-AM achieves better solutions on benchmark problems.

The adaptive scheme improves training efficiency for MLP and CNN models.

Abstract

Motivated by the potential for parallel implementation of batch-based algorithms and the accelerated convergence achievable with approximated second order information a limited memory version of the BFGS algorithm has been receiving increasing attention in recent years for large neural network training problems. As the shape of the cost function is generally not quadratic and only becomes approximately quadratic in the vicinity of a minimum, the use of second order information by L-BFGS can be unreliable during the initial phase of training, i.e. when far from a minimum. Therefore, to control the influence of second order information as training progresses, we propose a multi-batch L-BFGS algorithm, namely MB-AM, that gradually increases its trust in the curvature information by implementing a progressive storage and use of curvature data through a development-based increase (dev-increase) scheme. Using six discriminative modelling benchmark problems we show empirically that MB-AM has slightly faster convergence and, on average, achieves better solutions than the standard multi-batch L-BFGS algorithm when training MLP and CNN models.