  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.
