Efficient Second-Order Optimization for Neural Networks with Kernel Machines

Yawen Chen, Yile Chen, Jian Chen, Zeyi Wen, Jin Huang

Abstract: Second-order optimization has been recently explored in neural network training. However, the recomputation of the Hessian matrix in the second-order optimization posts much extra computation and memory burden in the training. There have been some attempts to address this issue by approximation on the Hessian matrix, which unfortunately degrades the performance of the neural models. In order to tackle this issue, we propose Kernel Stochastic Gradient Descent (Kernel SGD) which solves the optimization problem in a space transformed by the Hessian matrix of the kernel machine. Kernel SGD eliminates the Hessian matrix recomputation in the training and requires a much smaller memory cost which can be controlled via the mini-batch size. We show that Kernel SGD optimization is theoretically guaranteed to converge. Our experimental results on tabular, image and text data confirm that Kernel SGD converges up to 30 times faster than the existing second-order optimization techniques, and achieves the highest test accuracy on all the tasks tested. Kernel SGD even outperforms the first-order optimization baselines in some problems tested in our experiments.