Related papers: Solving Convex Smooth Function Constrained Optimiz…
Asynchronous stochastic gradient descent (ASGD) is a popular parallel optimization algorithm in machine learning. Most theoretical analysis on ASGD take a discrete view and prove upper bounds for their convergence rates. However, the…
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 revisit the use of Stochastic Gradient Descent (SGD) for solving convex optimization problems that serve as highly popular convex relaxations for many important low-rank matrix recovery problems such as \textit{matrix completion},…
We propose an accelerated version of stochastic variance reduced coordinate descent -- ASVRCD. As other variance reduced coordinate descent methods such as SEGA or SVRCD, our method can deal with problems that include a non-separable and…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
The alternating gradient descent (AGD) is a simple but popular algorithm which has been applied to problems in optimization, machine learning, data ming, and signal processing, etc. The algorithm updates two blocks of variables in an…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
In many modern machine learning applications, structures of underlying mathematical models often yield nonconvex optimization problems. Due to the intractability of nonconvexity, there is a rising need to develop efficient methods for…
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…
In this work we consider the stochastic minimization of nonsmooth convex loss functions, a central problem in machine learning. We propose a novel algorithm called Accelerated Nonsmooth Stochastic Gradient Descent (ANSGD), which exploits…
We propose a Riemannian version of Nesterov's Accelerated Gradient algorithm (RAGD), and show that for geodesically smooth and strongly convex problems, within a neighborhood of the minimizer whose radius depends on the condition number as…
Although Nesterov's accelerated gradient (NAG) methods have been studied from various perspectives, it remains unclear why the most popular forms of NAG must handle convex and strongly convex objective functions separately. Motivated by…
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…
The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…
Stochastic nested optimization, including stochastic compositional, min-max and bilevel optimization, is gaining popularity in many machine learning applications. While the three problems share the nested structure, existing works often…
We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a…
In this paper, we consider Nesterov's Accelerated Gradient method for solving Nonlinear Inverse and Ill-Posed Problems. Known to be a fast gradient-based iterative method for solving well-posed convex optimization problems, this method also…
Adaptive gradient methods, such as AdaGrad, are among the most successful optimization algorithms for neural network training. While these methods are known to achieve better dimensional dependence than stochastic gradient descent (SGD) for…
Performance analysis of first-order algorithms with inexact oracles has gained recent attention due to various emerging applications in which obtaining exact gradients is impossible or computationally expensive. Previous research has…
We develop a novel and single-loop variance-reduced algorithm to solve a class of stochastic nonconvex-convex minimax problems involving a nonconvex-linear objective function, which has various applications in different fields such as…