Related papers: A Proximal Stochastic Quasi-Newton Algorithm
In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…
We develop a trust-region method for minimizing the sum of a smooth term $f$ and a nonsmooth term $h$), both of which can be nonconvex. Each iteration of our method minimizes a possibly nonconvex model of $f + h$ in a trust region. The…
We propose a new first-order optimisation algorithm to solve high-dimensional non-smooth composite minimisation problems. Typical examples of such problems have an objective that decomposes into a non-smooth empirical risk part and a…
We consider a class of difference-of-convex (DC) optimization problems where the objective function is the sum of a smooth function and a possible nonsmooth DC function. The application of proximal DC algorithms to address this problem…
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 develop a class of algorithms, as variants of the stochastically controlled stochastic gradient (SCSG) methods (Lei and Jordan, 2016), for the smooth non-convex finite-sum optimization problem. Assuming the smoothness of each component,…
We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…
We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving empirical risk minimization (ERM) problems with a nonsmooth regularization term. Our algorithm is applicable…
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…
Quasi-Newton (QN) methods provide an efficient alternative to second-order methods for minimizing smooth unconstrained problems. While QN methods generally compose a Hessian estimate based on one secant interpolation per iteration,…
We consider the problem of minimizing a continuous function that may be nonsmooth and nonconvex, subject to bound constraints. We propose an algorithm that uses the L-BFGS quasi-Newton approximation of the problem's curvature together with…
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is…
This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…
We consider the problem of minimizing the average of a large number of smooth but possibly non-convex functions. In the context of most machine learning applications, each loss function is non-negative and thus can be expressed as the…
Most approximation methods in high dimensions exploit smoothness of the function being approximated. These methods provide poor convergence results for non-smooth functions with kinks. For example, such kinks can arise in the uncertainty…
The stochastic gradient descent has been widely used for solving composite optimization problems in big data analyses. Many algorithms and convergence properties have been developed. The composite functions were convex primarily and…
We present a stochastic setting for optimization problems with nonsmooth convex separable objective functions over linear equality constraints. To solve such problems, we propose a stochastic Alternating Direction Method of Multipliers…
We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…
We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that…