We revisit the choice of SGD for training deep neural networks by reconsidering the appropriate geometry in which to optimize the weights. We argue for a geometry invariant to rescaling of weights that does not affect the output of the network, and suggest Path-SGD, which is an approximate steepest descent method with respect to a path-wise regularizer related to max-norm regularization. Path-SGD is easy and efficient to implement and leads to empirical gains over SGD and AdaGrad.
Finally, REF propose a rescaling invariant path-wise regularizer and use it to derive Path-SGD, an approximate steepest descent with respect to the path-wise regularizer.
Path-SGD: Path-Normalized Optimization in Deep Neural Networks
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