Related papers: Stochastic Subspace Descent
For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…
In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods…
We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…
In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…
Stochastic gradient algorithms estimate the gradient based on only one or a few samples and enjoy low computational cost per iteration. They have been widely used in large-scale optimization problems. However, stochastic gradient algorithms…
A very popular approach for solving stochastic optimization problems is the stochastic gradient descent method (SGD). Although the SGD iteration is computationally cheap and the practical performance of this method may be satisfactory under…
The low-rank stochastic semidefinite optimization has attracted rising attention due to its wide range of applications. The nonconvex reformulation based on the low-rank factorization, significantly improves the computational efficiency but…
We consider gradient descent like algorithms for Support Vector Machine (SVM) training when the data is in relational form. The gradient of the SVM objective can not be efficiently computed by known techniques as it suffers from the…
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…
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…
Convergence of a projected stochastic gradient algorithm is demonstrated for convex objective functionals with convex constraint sets in Hilbert spaces. In the convex case, the sequence of iterates ${u_n}$ converges weakly to a point in the…
In decentralized learning, a network of nodes cooperate to minimize an overall objective function that is usually the finite-sum of their local objectives, and incorporates a non-smooth regularization term for the better generalization…
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…
We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…
We develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consists of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We introduce a new adaptive step-size strategy for convex optimization with stochastic gradient that exploits the local geometry of the objective function only by means of a first-order stochastic oracle and without any hyper-parameter…
We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a…
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…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…