Related papers: SAN: Stochastic Average Newton Algorithm for Minim…

In many contemporary optimization problems such as those arising in machine learning, it can be computationally challenging or even infeasible to evaluate an entire function or its derivatives. This motivates the use of stochastic…

Self-attributing neural networks (SANNs) present a potential path towards interpretable models for high-dimensional problems, but often face significant trade-offs in performance. In this work, we formally prove a lower bound on errors of…

Sample-average approximations (SAA) are a practical means of finding approximate solutions of stochastic programming problems involving an extremely large (or infinite) number of scenarios. SAA can also be used to find estimates of a lower…

We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed…

We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients.…

We consider the stochastic nested composition optimization problem where the objective is a composition of two expected-value functions. We proposed the stochastic ADMM to solve this complicated objective. In order to find an $\epsilon$…

A thesis submitted for the degree of Doctor of Philosophy of The Australian National University. In this work we introduce several new optimisation methods for problems in machine learning. Our algorithms broadly fall into two categories:…

Optimizing smooth convex functions in stochastic settings, where only noisy estimates of gradients and Hessians are available, is a fundamental problem in optimization. While first-order methods possess a low per-iteration cost, their…

We present a stochastic optimization method that uses a fourth-order regularized model to find local minima of smooth and potentially non-convex objective functions with a finite-sum structure. This algorithm uses sub-sampled derivatives…

The Newton's method for solving stationary Navier-Stokes equations (NSE) is known to convergent fast, however, may fail due to a bad initial guess. This work presents a simple-to-implement nonlinear preconditioning of Newton's iteration,…

In computational science workflows, it is often the case that 1) objective functions for optimization involve multiple simulation outputs, and 2) those simulations can be performed (at least partially) in parallel. In this work, we…

Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…

In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…

Motivated by applications in optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving stochastic optimization problems. In the literature, the convergence analysis of these algorithms relies on strong…

We study stochastic second-order methods for solving general non-convex optimization problems. We propose using a special version of momentum to stabilize the stochastic gradient and Hessian estimates in Newton's method. We show that…

We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…

We develop a fast and robust algorithm for solving large scale convex composite optimization models with an emphasis on the $\ell_1$-regularized least squares regression (Lasso) problems. Despite the fact that there exist a large number of…

We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…

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…

This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…