相关论文: Accelerated Multiplicative Weights Update Avoids S…

In this work, we study the asymptotic randomness of an algorithmic estimator of the saddle point of a globally convex-concave and locally strongly-convex strongly-concave objective. Specifically, we show that the averaged iterates of a…

We propose a regularized saddle-point algorithm for convex networked optimization problems with resource allocation constraints. Standard distributed gradient methods suffer from slow convergence and require excessive communication when…

We develop a new consensus-based distributed algorithm for solving learning problems with feature partitioning and non-smooth convex objective functions. Such learning problems are not separable, i.e., the associated objective functions…

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided for example by means of stochastic gradient descent methods. In this work, we provide…

We consider the problem of finding critical points of functions that are non-convex and non-smooth. Studying a fairly broad class of such problems, we analyze the behavior of three gradient-based methods (gradient descent, proximal update,…

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 develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…

We show that on the manifold of fixed-rank and symmetric positive semi-definite matrices, the Riemannian gradient descent algorithm almost surely escapes some spurious critical points on the boundary of the manifold. Our result is the first…

Federated learning (FL) approaches for saddle point problems (SPP) have recently gained in popularity due to the critical role they play in machine learning (ML). Existing works mostly target smooth unconstrained objectives in Euclidean…

In this work, we analyze two of the most fundamental algorithms in geodesically convex optimization: Riemannian gradient descent and (possibly inexact) Riemannian proximal point. We quantify their rates of convergence and produce different…

Adaptive methods such as Adam and RMSProp are widely used in deep learning but are not well understood. In this paper, we seek a crisp, clean and precise characterization of their behavior in nonconvex settings. To this end, we first…

In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence…

This study introduces two second-order methods designed to provably avoid saddle points in composite nonconvex optimization problems: (i) a nonsmooth trust-region method and (ii) a curvilinear linesearch method. These developments are…

We propose two variants of the Primal Dual Hybrid Gradient (PDHG) algorithm for saddle point problems with block decomposable duals, hereafter called Multi-Timescale PDHG (MT-PDHG) and its accelerated variant (AMT-PDHG). Through novel…

The note considers normalized gradient descent (NGD), a natural modification of classical gradient descent (GD) in optimization problems. A serious shortcoming of GD in non-convex problems is that GD may take arbitrarily long to escape from…

Motivated by energy based analyses for descent methods in the Euclidean setting, we investigate a generalisation of such analyses for descent methods over Riemannian manifolds. In doing so, we find that it is possible to derive…

The Frank-Wolfe algorithm is a classic method for constrained optimization problems. It has recently been popular in many machine learning applications because its projection-free property leads to more efficient iterations. In this paper,…

This paper considers the problem of understanding the behavior of a general class of accelerated gradient methods on smooth nonconvex functions. Motivated by some recent works that have proposed effective algorithms, based on Polyak's heavy…

We study the unconstrained and the minimax saddle point variants of the convex multi-stage stochastic programming problem, where consecutive decisions are coupled through the objective functions, rather than through the constraints. We…

We study a class of misspecified saddle point (SP) problems, where the optimization objective depends on an unknown parameter that must be learned concurrently from data. Unlike existing studies that assume parameters are fully known or…