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Recently, research on accelerated stochastic gradient descent methods (e.g., SVRG) has made exciting progress (e.g., linear convergence for strongly convex problems). However, the best-known methods (e.g., Katyusha) requires at least two…
This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…
This paper describes a novel algorithmic framework to minimize a finite-sum of functions available over a network of nodes. The proposed framework, that we call~\GTVR, is stochastic and decentralized, and thus is particularly suitable for…
In this paper, we propose a simple variant of the original SVRG, called variance reduced stochastic gradient descent (VR-SGD). Unlike the choices of snapshot and starting points in SVRG and its proximal variant, Prox-SVRG, the two vectors…
Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…
We prove convergence of a single time-scale stochastic subgradient method with subgradient averaging for constrained problems with a nonsmooth and nonconvex objective function having the property of generalized differentiability. As a tool…
We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without requiring any boundedness or control of the variance of the…
In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology optimization and convergence rates. In contrast to standard stochastic gradient optimization…
In this contribution, we present a full overview of the continuous stochastic gradient (CSG) method, including convergence results, step size rules and algorithmic insights. We consider optimization problems in which the objective function…
Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…
In this paper we propose several adaptive gradient methods for stochastic optimization. Unlike AdaGrad-type of methods, our algorithms are based on Armijo-type line search and they simultaneously adapt to the unknown Lipschitz constant of…
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…
We introduce a novel algorithm for gradient-based optimization of stochastic objective functions. The method may be seen as a variant of SGD with momentum equipped with an adaptive learning rate automatically adjusted by an 'energy'…
Communication has been seen as a significant bottleneck in industrial applications over large-scale networks. To alleviate the communication burden, sign-based optimization algorithms have gained popularity recently in both industrial and…
Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss…
Stochastic gradient algorithms have been the main focus of large-scale learning problems and they led to important successes in machine learning. The convergence of SGD depends on the careful choice of learning rate and the amount of the…
Conjugate Gradient (CG) methods are one of the most effective iterative methods to solve linear equations in Hilbert spaces. So far, they have been inherently bound to these spaces since they make use of the inner product structure. In more…
We present and analyze several strategies for improving the performance of stochastic variance-reduced gradient (SVRG) methods. We first show that the convergence rate of these methods can be preserved under a decreasing sequence of errors…
Stochastic convex optimization algorithms are the most popular way to train machine learning models on large-scale data. Scaling up the training process of these models is crucial, but the most popular algorithm, Stochastic Gradient Descent…
The method of nonlinear conjugate gradients (NCG) is widely used in practice for unconstrained optimization, but it satisfies weak complexity bounds at best when applied to smooth convex functions. In contrast, Nesterov's accelerated…