A Stochastic Proximal Method for Nonsmooth Regularized Finite Sum Optimization

• URL: http://arxiv.org/abs/2206.06531v1
• Date: Tue, 14 Jun 2022 00:28:44 GMT
• Title: A Stochastic Proximal Method for Nonsmooth Regularized Finite Sum Optimization
• Authors: Dounia Lakhmiri and Dominique Orban and Andrea Lodi
• Abstract summary: We consider the problem of training a deep neural network with nonsmooth regularization to retrieve a sparse sub-structure. We derive a new solver, called SR2, whose convergence and worst-case complexity are established without knowledge or approximation of the gradient's Lipschitz constant. Experiments on network instances trained on CIFAR-10 and CIFAR-100 show that SR2 consistently achieves higher sparsity and accuracy than related methods such as ProxGEN and ProxSGD.
• Score: 7.014966911550542
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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