Related papers: Fast Unconstrained Optimization via Hessian Averag…

We establish the O($\frac{1}{k}$) convergence rate for distributed stochastic gradient methods that operate over strongly convex costs and random networks. The considered class of methods is standard each node performs a weighted average of…

Stochastic optimization algorithms with variance reduction have proven successful for minimizing large finite sums of functions. Unfortunately, these techniques are unable to deal with stochastic perturbations of input data, induced for…

The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…

This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the…

We introduce a hybrid stochastic estimator to design stochastic gradient algorithms for solving stochastic optimization problems. Such a hybrid estimator is a convex combination of two existing biased and unbiased estimators and leads to…

We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…

In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…

This report investigates the fitting of the Hessian or its inverse for stochastic optimizations using a Hessian fitting criterion derived from the preconditioned stochastic gradient descent (PSGD) method. This criterion is closely related…

Motivated by applications arising from large scale optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving unconstrained convex optimization problems. The convergence analysis of the SQN methods,…

Dual descent methods are commonly used to solve network flow optimization problems, since their implementation can be distributed over the network. These algorithms, however, often exhibit slow convergence rates. Approximate Newton methods…

Gradient descent is the primary workhorse for optimizing large-scale problems in machine learning. However, its performance is highly sensitive to the choice of the learning rate. A key limitation of gradient descent is its lack of natural…

This work concerns the local convergence theory of Newton and quasi-Newton methods for convex-composite optimization: minimize f(x):=h(c(x)), where h is an infinite-valued proper convex function and c is C^2-smooth. We focus on the case…

Motivated by recent developments in serverless systems for large-scale computation as well as improvements in scalable randomized matrix algorithms, we develop OverSketched Newton, a randomized Hessian-based optimization algorithm to solve…

We propose a new stochastic proximal quasi-Newton method for minimizing the sum of two convex functions in the particular context that one of the functions is the average of a large number of smooth functions and the other one is nonsmooth.…

The incremental gradient method is a prominent algorithm for minimizing a finite sum of smooth convex functions, used in many contexts including large-scale data processing applications and distributed optimization over networks. It is a…

In this paper, we present new second-order algorithms for composite convex optimization, called Contracting-domain Newton methods. These algorithms are affine-invariant and based on global second-order lower approximation for the smooth…

The performance of optimization methods is often tied to the spectrum of the objective Hessian. Yet, conventional assumptions, such as smoothness, do often not enable us to make finely-grained convergence statements -- particularly not for…

A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory…

We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…

We consider minimization of composite functions of the form $f(g(x))+h(x)$, where $f$ and $h$ are convex functions (which can be nonsmooth) and $g$ is a smooth vector mapping. In addition, we assume that $g$ is the average of finite number…