Related papers: Non-asymptotic Analysis of Stochastic Methods for …

Difference of convex (DC) functions cover a broad family of non-convex and possibly non-smooth and non-differentiable functions, and have wide applications in machine learning and statistics. Although deterministic algorithms for DC…

In this paper, we investigate the non-asymptotic stationary convergence behavior of Stochastic Mirror Descent (SMD) for nonconvex optimization. We focus on a general class of nonconvex nonsmooth stochastic optimization problems, in which…

Non-convex optimization problems are ubiquitous in machine learning, especially in Deep Learning. While such complex problems can often be successfully optimized in practice by using stochastic gradient descent (SGD), theoretical analysis…

We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

With the large rising of complex data, the nonconvex models such as nonconvex loss function and nonconvex regularizer are widely used in machine learning and pattern recognition. In this paper, we propose a class of mini-batch stochastic…

We propose a novel stochastic smoothing accelerated gradient (SSAG) method for general constrained nonsmooth convex composite optimization, and analyze the convergence rates. The SSAG method allows various smoothing techniques, and can deal…

We consider the problem of minimizing the sum of three convex functions: i) a smooth function $f$ in the form of an expectation or a finite average, ii) a non-smooth function $g$ in the form of a finite average of proximable functions…

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…

Over the past ten years, driven by large scale optimisation problems arising from machine learning, the development of stochastic optimisation methods have witnessed a tremendous growth. However, despite their popularity, the theoretical…

Structured non-convex learning problems, for which critical points have favorable statistical properties, arise frequently in statistical machine learning. Algorithmic convergence and statistical estimation rates are well-understood for…

In this paper, we propose a new SVRG-style acceleated stochastic algorithm for solving a family of non-convex optimization problems whose objective consists of a sum of $n$ smooth functions and a non-smooth convex function. Our major goal…

Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…

We present a novel class of projected gradient (PG) methods for minimizing a smooth but not necessarily convex function over a convex compact set. We first provide a novel analysis of the constant-stepsize PG method, achieving the…

We propose and analyze several stochastic gradient algorithms for finding stationary points or local minimum in nonconvex, possibly with nonsmooth regularizer, finite-sum and online optimization problems. First, we propose a simple proximal…

The stochastic proximal point (SPP) methods have gained recent attention for stochastic optimization, with strong convergence guarantees and superior robustness to the classic stochastic gradient descent (SGD) methods showcased at little to…

Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…

Motivated by penalized likelihood maximization in complex models, we study optimization problems where neither the function to optimize nor its gradient have an explicit expression, but its gradient can be approximated by a Monte Carlo…

This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…

Many recent applications in machine learning and data fitting call for the algorithmic solution of structured smooth convex optimization problems. Although the gradient descent method is a natural choice for this task, it requires exact…