2019/11/15 by Laura Palagi, Ruggiero Seccia · 3 citations
Computer Science · Mathematics · #Advanced Neural Network Applications #Artificial neural network #Block (permutation group theory) #Coordinate descent #Domain Adaptation and Few-Shot Learning #Feed forward #Feedforward neural network #Generalization #Optimization problem #Scheme (mathematics) #Stochastic Gradient Optimization Techniques #Training (meteorology) #cs.LG #math.OC
paper · pdf · doi:10.1007/s10898-019-00856-0
published in Journal of Global Optimization 77(1), 97-124 (Springer Science+Business Media) · 23 pages. J Glob Optim (2019)
openalex publication_date 2019/11/15 · openalex created_date 2019/11/22 · arxiv created 2020/03/18 · arxiv updated 2020/06/16 · openalex updated_date 2026/08/05
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 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.