Related papers: Estimate Sequences for Variance-Reduced Stochastic…
We consider a class of stochastic smooth convex optimization problems under rather general assumptions on the noise in the stochastic gradient observation. As opposed to the classical problem setting in which the variance of noise is…
We provide the first theoretical analysis on the convergence rate of the asynchronous stochastic variance reduced gradient (SVRG) descent algorithm on non-convex optimization. Recent studies have shown that the asynchronous stochastic…
Stochastic Gradient Descent-Ascent (SGDA) is one of the most prominent algorithms for solving min-max optimization and variational inequalities problems (VIP) appearing in various machine learning tasks. The success of the method led to…
We propose a new first-order optimization algorithm -- AcceleratedGradient-OptimisticGradient (AG-OG) Descent Ascent -- for separable convex-concave minimax optimization. The main idea of our algorithm is to carefully leverage the structure…
This paper presents a sufficient condition for stochastic gradients not to slow down the convergence of Nesterov's accelerated gradient method. The new condition has the strong-growth condition by Schmidt \& Roux as a special case, and it…
We introduce a novel and efficient algorithm called the stochastic approximate gradient descent (SAGD), as an alternative to the stochastic gradient descent for cases where unbiased stochastic gradients cannot be trivially obtained.…
We consider solving a convex, possibly stochastic optimization problem over a randomly time-varying multi-agent network. Each agent has access to some local objective function, and it only has unbiased estimates of the gradients of the…
Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…
Despite the rise to fame of incremental variance-reduced methods in recent years, their use in nonsmooth optimization is still limited to few simple cases. This is due to the fact that existing methods require to evaluate the proximity…
We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…
We focus on analyzing the classical stochastic projected gradient methods under a general dependent data sampling scheme for constrained smooth nonconvex optimization. We show the worst-case rate of convergence $\tilde{O}(t^{-1/4})$ and…
This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…
We propose a remarkably general variance-reduced method suitable for solving regularized empirical risk minimization problems with either a large number of training examples, or a large model dimension, or both. In special cases, our method…
This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We…
We expose in a tutorial fashion the mechanisms which underlie the synthesis of optimization algorithms based on dynamic integral quadratic constraints. We reveal how these tools from robust control allow to design accelerated gradient…
Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
We introduce a clipping strategy for Stochastic Gradient Descent (SGD) which uses quantiles of the gradient norm as clipping thresholds. We prove that this new strategy provides a robust and efficient optimization algorithm for smooth…
Stochastic gradient algorithms are the main focus of large-scale optimization problems and led to important successes in the recent advancement of the deep learning algorithms. The convergence of SGD depends on the careful choice of…
We propose and analyze a new stochastic gradient method, which we call Stochastic Unbiased Curvature-aided Gradient (SUCAG), for finite sum optimization problems. SUCAG constitutes an unbiased total gradient tracking technique that uses…