PathProx: A Proximal Gradient Algorithm for Weight Decay Regularized Deep Neural Networks
This work addresses optimization bottlenecks for deep learning practitioners, offering a faster training method for weight decay regularization, though it is incremental as it builds on existing regularization techniques.
The paper tackles the inefficiency of stochastic gradient descent for weight decay regularization in deep neural networks by proposing PathProx, a proximal gradient algorithm based on an equivalent regularization formulation, which converges much faster to sparse solutions.
Weight decay is one of the most widely used forms of regularization in deep learning, and has been shown to improve generalization and robustness. The optimization objective driving weight decay is a sum of losses plus a term proportional to the sum of squared weights. This paper argues that stochastic gradient descent (SGD) may be an inefficient algorithm for this objective. For neural networks with ReLU activations, solutions to the weight decay objective are equivalent to those of a different objective in which the regularization term is instead a sum of products of $\ell_2$ (not squared) norms of the input and output weights associated with each ReLU neuron. This alternative (and effectively equivalent) regularization suggests a novel proximal gradient algorithm for network training. Theory and experiments support the new training approach, showing that it can converge much faster to the sparse solutions it shares with standard weight decay training.