Related papers: Non-convex Finite-Sum Optimization Via SCSG Method…
We analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly…
Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
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 study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient…
Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…
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 propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in…
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…
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…
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 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…
Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…
In this paper, we proposed a new technique, {\em variance controlled stochastic gradient} (VCSG), to improve the performance of the stochastic variance reduced gradient (SVRG) algorithm. To avoid over-reducing the variance of gradient by…
Large-scale nonconvex optimization problems are ubiquitous in modern machine learning, and among practitioners interested in solving them, Stochastic Gradient Descent (SGD) reigns supreme. We revisit the analysis of SGD in the nonconvex…
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…
In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems.…
Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…
The stochastic composition optimization proposed recently by Wang et al. [2014] minimizes the objective with the compositional expectation form: $\min_x~(\mathbb{E}_iF_i \circ \mathbb{E}_j G_j)(x).$ It summarizes many important applications…
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…