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We present two sampled quasi-Newton methods (sampled LBFGS and sampled LSR1) for solving empirical risk minimization problems that arise in machine learning. Contrary to the classical variants of these methods that sequentially build Hessian or inverse Hessian approximations as the optimization progresses, our proposed methods sample points randomly around the current iterate at every iteration to produce these approximations. As a result, the approximations constructed make use of more reliable (recent and local) information, and do not depend on past iterate information that could be significantly stale. Our proposed algorithms are efficient in terms of accessed data points (epochs) and have enough concurrency to take advantage of parallel/distributed computing environments. We provide convergence guarantees for our proposed methods. Numerical tests on a toy classification problem as well as on popular benchmarking binary classification and neural network training tasks reveal that the methods outperform their classical variants.
In this paper, we propose some new proximal quasi-Newton methods with line search or without line search for a special class of nonsmooth multiobjective optimization problems, where each objective function is the sum of a twice continuously different
In this paper, we follow the work (Rodomanov and Nesterov 2021) to study quasi-Newton methods, which is based on the updating formulas from a certain subclass of the Broyden family. We focus on the common SR1 and BFGS quasi-Newton methods to establis
In this paper, we consider stochastic second-order methods for minimizing a finite summation of nonconvex functions. One important key is to find an ingenious but cheap scheme to incorporate local curvature information. Since the true Hessian matrix
The standard L-BFGS method relies on gradient approximations that are not dominated by noise, so that search directions are descent directions, the line search is reliable, and quasi-Newton updating yields useful quadratic models of the objective fun
We consider the use of a curvature-adaptive step size in gradient-based iterative methods, including quasi-Newton methods, for minimizing self-concordant functions, extending an approach first proposed for Newtons method by Nesterov. This step size h