Related papers: Adaptive Conditional Gradient Sliding: Projection-…
The Conditional Gradient Method is generalized to a class of non-smooth non-convex optimization problems with many applications in machine learning. The proposed algorithm iterates by minimizing so-called model functions over the constraint…
This paper introduces new parameter-free first-order methods for convex optimization problems in which the objective function exhibits H\"{o}lder smoothness. Inspired by the recently proposed distance-over-gradient (DOG) technique, we…
In this paper, we generalize the well-known Nesterov's accelerated gradient (AG) method, originally designed for convex smooth optimization, to solve nonconvex and possibly stochastic optimization problems. We demonstrate that by properly…
Minimax optimization recently is widely applied in many machine learning tasks such as generative adversarial networks, robust learning and reinforcement learning. In the paper, we study a class of nonconvex-nonconcave minimax optimization…
Gradient-based minimax optimal algorithms have greatly promoted the development of continuous optimization and machine learning. One seminal work due to Yurii Nesterov [Nes83a] established $\tilde{\mathcal{O}}(\sqrt{L/\mu})$ gradient…
While Nesterov's Accelerated Gradient Descent (AGD) efficiently solves constrained problems when the constraint set $X \subseteq \mathbb{R}^n$ is simple and easy to project onto, it remains an open question whether function-constrained…
This work proposes A$^2$GD, a novel adaptive accelerated gradient descent method for convex and composite optimization. Smoothness and convexity constants are updated via Lyapunov analysis. Inspired by stability analysis in ODE solvers, the…
This paper introduces adaptive Bregman proximal gradient algorithms for solving convex composite minimization problems without relying on global relative smoothness or strong convexity assumptions. Building upon recent advances in adaptive…
We suggest a simple adaptive step-size procedure, which does not require any line-search, for a general class of nonlinear optimization methods and prove convergence of a general method under mild assumptions. In particular, the goal…
We investigate a projection free method, namely conditional gradient sliding on batched, stochastic and finite-sum non-convex problem. CGS is a smart combination of Nesterov's accelerated gradient method and Frank-Wolfe (FW) method, 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…
In this paper, we study the stochastic gradient descent (SGD) method for the nonconvex nonsmooth optimization, and propose an accelerated SGD method by combining the variance reduction technique with Nesterov's extrapolation technique.…
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…
In this work, we propose a novel adaptive stochastic gradient-free (ASGF) approach for solving high-dimensional nonconvex optimization problems based on function evaluations. We employ a directional Gaussian smoothing of the target function…
We propose a new family of adaptive first-order methods for a class of convex minimization problems that may fail to be Lipschitz continuous or smooth in the standard sense. Specifically, motivated by a recent flurry of activity on…
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…
Adaptive gradient algorithms perform gradient-based updates using the history of gradients and are ubiquitous in training deep neural networks. While adaptive gradient methods theory is well understood for minimization problems, the…
Recent studies have shown that many nonconvex machine learning problems satisfy a generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms are not fully adapted to such…
Constrained second-order convex optimization algorithms are the method of choice when a high accuracy solution to a problem is needed, due to their local quadratic convergence. These algorithms require the solution of a constrained…
We present a modification of the conditional gradient sliding (CGS) method that was originally developed in \cite{lan2016conditional}. While the CGS method is a theoretical breakthrough in the theory of projection-free first-order methods…