Related papers: Stochastic Second-Order Optimization via von Neuma…
We show that, for finite-sum minimization problems, incorporating partial second-order information of the objective function can dramatically improve the robustness to mini-batch size of variance-reduced stochastic gradient methods, making…
In this paper, we generalize (accelerated) Newton's method with cubic regularization under inexact second-order information for (strongly) convex optimization problems. Under mild assumptions, we provide global rate of convergence of these…
An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…
This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(\sigma / \sqrt{T})$ convergence when the oracle feedback is stochastic with variance $\sigma^2$,…
Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention…
Second-order optimization methods offer notable advantages in training deep neural networks by utilizing curvature information to achieve faster convergence. However, traditional second-order techniques are computationally prohibitive,…
Approximate second-order optimization methods often exhibit poorer generalization compared to first-order approaches. In this work, we look into this issue through the lens of the loss landscape and find that existing second-order methods…
This paper studies stochastic minimization of a finite-sum loss $ F (\mathbf{x}) = \frac{1}{N} \sum_{\xi=1}^N f(\mathbf{x};\xi) $. In many real-world scenarios, the Hessian matrix of such objectives exhibits a low-rank structure on a batch…
We develop a new efficient sequential approximate leverage score algorithm, SALSA, using methods from randomized numerical linear algebra (RandNLA) for large matrices. We demonstrate that, with high probability, the accuracy of SALSA's…
We present novel algorithms for simulation optimization using random directions stochastic approximation (RDSA). These include first-order (gradient) as well as second-order (Newton) schemes. We incorporate both continuous-valued as well as…
Optimization of convex functions under stochastic zeroth-order feedback has been a major and challenging question in online learning. In this work, we consider the problem of optimizing second-order smooth and strongly convex functions…
In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…
We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the…
Two-time-scale stochastic approximation algorithms are iterative methods used in applications such as optimization, reinforcement learning, and control. Finite-time analysis of these algorithms has primarily focused on fixed point…
In this paper, we propose a distributed stochastic second-order proximal method that enables agents in a network to cooperatively minimize the sum of their local loss functions without any centralized coordination. The proposed algorithm,…
We present a novel statistical inference framework for convex empirical risk minimization, using approximate stochastic Newton steps. The proposed algorithm is based on the notion of finite differences and allows the approximation of a…
We study stochastic optimization of nonconvex loss functions, which are typical objectives for training neural networks. We propose stochastic approximation algorithms which optimize a series of regularized, nonlinearized losses on large…
We investigate the problem of sequential linear data prediction for real life big data applications. The second order algorithms, i.e., Newton-Raphson Methods, asymptotically achieve the performance of the "best" possible linear data…
A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…
For the approximation and simulation of twofold iterated stochastic integrals and the corresponding L\'{e}vy areas w.r.t. a multi-dimensional Wiener process, we review four algorithms based on a Fourier series approach. Especially, the very…