Training Deep Neural Networks via Optimization Over Graphs

In this work, we propose to train a deep neural network by distributed optimization over a graph. Two nonlinear functions are considered: the rectified linear unit (ReLU) and a linear unit with both lower and upper cutoffs (DCutLU). The problem reformulation over a graph is realized by explicitly representing ReLU or DCutLU using a set of slack variables. We then apply the alternating direction method of multipliers (ADMM) to update the weights of the network layer-wise by solving subproblems of the reformulated problem. Empirical results suggest that the ADMM-based method is less sensitive to overfitting than the stochastic gradient descent (SGD) and Adam methods.