Convergent Block Coordinate Descent for Training Tikhonov Regularized Deep Neural Networks

Ziming Zhang; Matthew Brand

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arXiv · 1711.07354

Convergent Block Coordinate Descent for Training Tikhonov Regularized Deep Neural Networks

Ziming Zhang·Matthew Brand

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Abstract

By lifting the ReLU function into a higher dimensional space, we develop a smooth multi-convex formulation for training feed-forward deep neural networks (DNNs). This allows us to develop a block coordinate descent (BCD) training algorithm consisting of a sequence of numerically well-behaved convex optimizations. Using ideas from proximal point methods in convex analysis, we prove that this BCD algorithm will converge globally to a stationary point with R-linear convergence rate of order one. In experiments with the MNIST database, DNNs trained with this BCD algorithm consistently yielded better test-set error rates than identical DNN architectures trained via all the stochastic gradient descent (SGD) variants in the Caffe toolbox.

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BibTeX RIS

Ziming Zhang, Matthew Brand. 2017-11-20. Convergent Block Coordinate Descent for Training Tikhonov Regularized Deep Neural Networks. https://arxiv.org/abs/1711.07354

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