A stochastic proximal method for nonsmooth regularized finite sum optimization

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We consider the problem of training a deep neural network with nonsmooth regularization to retrieve a sparse and efficient sub-structure. Our regularizer is only assumed to be lower semi-continuous and prox-bounded. We combine an adaptive quadratic regularization approach with proximal stochastic gradient principles to derive a new solver, called SR2, whose convergence and worst-case complexity are established without knowledge or approximation of the gradient's Lipschitz constant. We formulate a stopping criteria that ensures an appropriate first-order stationarity measure converges to zero under certain conditions. We establish a worst-case iteration complexity of \(\mathcal{O}(\epsilon^{-2})\) that matches those of related methods like ProxGEN, where the learning rate is assumed to be related to the Lipschitz constant. Our experiments on network instances trained on CIFAR-10 and CIFAR-100 with \(\ell_1\) and \(\ell_0\) regularizations show that SR2 consistently achieves higher sparsity and accuracy than related methods such as ProxGEN and ProxSGD.

, 17 pages

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