  Deep Feedforward Neural Networks' (DFNNs) weights estimation relies on the
solution of a very large nonconvex optimization problem that may have many
local (no global) minimizers, saddle points and large plateaus. As a
consequence, optimization algorithms can be attracted toward local minimizers
which can lead to bad solutions or can slow down the optimization process.
Furthermore, the time needed to find good solutions to the training problem
depends on both the number of samples and the number of variables. In this
work, we show how Block Coordinate Descent (BCD) methods can be applied to
improve performance of state-of-the-art algorithms by avoiding bad stationary
points and flat regions. We first describe a batch BCD method ables to
effectively tackle the network's depth and then we further extend the algorithm
proposing a \textit{minibatch} BCD framework able to scale with respect to both
the number of variables and the number of samples by embedding a BCD approach
into a minibatch framework. By extensive numerical results on standard datasets
for several architecture networks, we show how the application of BCD methods
to the training phase of DFNNs permits to outperform standard batch and
minibatch algorithms leading to an improvement on both the training phase and
the generalization performance of the networks.
