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We identify and analyze a fundamental limitation of the classical projected subgradient method in nonsmooth convex optimization: the inevitable failure caused by the absence of valid subgradients at boundary points. We show that, under…
In this paper, we propose the approximate Bregman proximal gradient algorithm (ABPG) for solving composite nonconvex optimization problems. ABPG employs a new distance that approximates the Bregman distance, making the subproblem of ABPG…
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…
In this paper, we consider a class of finite-sum convex optimization problems whose objective function is given by the summation of $m$ ($\ge 1$) smooth components together with some other relatively simple terms. We first introduce a…
Our main goal in this paper is to show that one can skip gradient computations for gradient descent type methods applied to certain structured convex programming (CP) problems. To this end, we first present an accelerated gradient sliding…
We introduce a generic scheme to solve nonconvex optimization problems using gradient-based algorithms originally designed for minimizing convex functions. Even though these methods may originally require convexity to operate, the proposed…
Stochastic gradient methods (SGMs) have been extensively used for solving stochastic problems or large-scale machine learning problems. Recent works employ various techniques to improve the convergence rate of SGMs for both convex and…
Adaptive gradient methods, which adopt historical gradient information to automatically adjust the learning rate, despite the nice property of fast convergence, have been observed to generalize worse than stochastic gradient descent (SGD)…
Backtracking linesearch is the de facto approach for minimizing continuously differentiable functions with locally Lipschitz gradient. In recent years, it has been shown that in the convex setting it is possible to avoid linesearch…
In this paper, we study the problem of maximizing continuous submodular functions that naturally arise in many learning applications such as those involving utility functions in active learning and sensing, matrix approximations and network…
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…
Adaptive gradient methods, such as AdaGrad, have become fundamental tools in deep learning. Despite their widespread use, the asymptotic convergence of AdaGrad remains poorly understood in non-convex scenarios. In this work, we present the…
In this thesis we develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive…
Adaptive gradient methods, especially Adam-type methods (such as Adam, AMSGrad, and AdaBound), have been proposed to speed up the training process with an element-wise scaling term on learning rates. However, they often generalize poorly…
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…
Min-max optimization is emerging as a key framework for analyzing problems of robustness to strategically and adversarially generated data. We propose a random reshuffling-based gradient free Optimistic Gradient Descent-Ascent algorithm for…
Stochastic gradient methods (SGMs) have been widely used for solving stochastic optimization problems. A majority of existing works assume no constraints or easy-to-project constraints. In this paper, we consider convex stochastic…
This paper investigates a novel gradient algorithm, AGEM, using both energy and momentum, for addressing general non-convex optimization problems. The solution properties of the AGEM algorithm, including aspects such as uniformly…
We suggest simple modifications of the conditional gradient method for smooth optimization problems, which maintain the basic convergence properties, but reduce the implementation cost of each iteration essentially. Namely, we propose the…
Recent efforts to accelerate first-order methods have focused on convex optimization problems that satisfy a geometric property known as error-bound condition, which covers a broad class of problems, including piece-wise linear programs and…