相关论文: Robust Accelerated Primal-Dual Methods for Computi…

We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP…

In this paper, we give a sharp analysis for Stochastic Gradient Descent (SGD) and prove that SGD is able to efficiently escape from saddle points and find an $(\epsilon, O(\epsilon^{0.5}))$-approximate second-order stationary point in…

We present a novel, practical, and provable approach for solving diagonally constrained semi-definite programming (SDP) problems at scale using accelerated non-convex programming. Our algorithm non-trivially combines acceleration motions…

Adversarial neural networks solve many important problems in data science, but are notoriously difficult to train. These difficulties come from the fact that optimal weights for adversarial nets correspond to saddle points, and not…

Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…

We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…

We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…

We consider stochastic convex optimization problems with affine constraints and develop several methods using either primal or dual approach to solve it. In the primal case, we use a special penalization technique to make the initial…

In this paper we propose an efficient distributed algorithm for solving loosely coupled convex optimization problems. The algorithm is based on a primal-dual interior-point method in which we use the alternating direction method of…

We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…

We present a comprehensive theoretical analysis of first-order methods for escaping strict saddle points in smooth non-convex optimization. Our main contribution is a Perturbed Saddle-escape Descent (PSD) algorithm with fully explicit…

In this paper, we explore a broad class of constrained saddle point problems with a bilevel structure, wherein the upper-level objective function is nonconvex-concave and smooth over compact and convex constraint sets, subject to a strongly…

We propose an accelerated forward-backward method with fast convergence rate for finding a minimizer of a decomposable nonsmooth convex function over a closed convex set, and name it smoothing accelerated proximal gradient (SAPG) algorithm.…

We provide a simple and generic adaptive restart scheme for convex optimization that is able to achieve worst-case bounds matching (up to constant multiplicative factors) optimal restart schemes that require knowledge of problem specific…

We present Scaff-PD, a fast and communication-efficient algorithm for distributionally robust federated learning. Our approach improves fairness by optimizing a family of distributionally robust objectives tailored to heterogeneous clients.…

We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…

Reinforcement learning is widely used in applications where one needs to perform sequential decisions while interacting with the environment. The problem becomes more challenging when the decision requirement includes satisfying some safety…

The optimistic gradient method has seen increasing popularity for solving convex-concave saddle point problems. To analyze its iteration complexity, a recent work [arXiv:1906.01115] proposed an interesting perspective that interprets this…

In this paper, for a convex-concave bilinear saddle point problem, we propose a Tikhonov regularized second-order primal-dual dynamical system with slow damping, extrapolation and general time scaling parameters. Depending on the vanishing…

We propose an alternating subgradient method with non-constant step sizes for solving convex-concave saddle-point problems associated with general convex-concave functions. We assume that the sequence of our step sizes is not summable but…