Related papers: On Convergence Analysis of Network-GIANT: An appro…

We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. Recent advances using the distributed gradient…

This paper studies probabilistic rates of convergence for consensus+innovations type of algorithms in random, generic networks. For each node, we find a lower and also a family of upper bounds on the large deviations rate function, thus…

This paper considers distributed optimization problems, where each agent cooperatively minimizes the sum of local objective functions through the communication with its neighbors. The widely adopted distributed gradient method in solving…

We show that Newton's method converges globally at a linear rate for objective functions whose Hessians are stable. This class of problems includes many functions which are not strongly convex, such as logistic regression. Our linear…

We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…

We study a distributed consensus-based stochastic gradient descent (SGD) algorithm and show that the rate of convergence involves the spectral properties of two matrices: the standard spectral gap of a weight matrix from the network…

Stochastic variance reduced methods have gained a lot of interest recently for empirical risk minimization due to its appealing run time complexity. When the data size is large and disjointly stored on different machines, it becomes…

In this work, we study the task of distributed optimization over a network of learners in which each learner possesses a convex cost function, a set of affine equality constraints, and a set of convex inequality constraints. We propose a…

In this paper we consider a distributed convex optimization problem over time-varying undirected networks. We propose a dual method, primarily averaged network dual ascent (PANDA), that is proven to converge R-linearly to the optimal point…

This paper investigates the global convergence of stepsized Newton methods for convex functions with H\"older continuous Hessians or third derivatives. We propose several simple stepsize schedules with fast global convergence guarantees, up…

This paper establishes risk convergence and asymptotic weight matrix alignment --- a form of implicit regularization --- of gradient flow and gradient descent when applied to deep linear networks on linearly separable data. In more detail,…

We consider a distributed learning setup where a sparse signal is estimated over a network. Our main interest is to save communication resource for information exchange over the network and reduce processing time. Each node of the network…

We study distributed composite optimization over networks: agents minimize a sum of smooth (strongly) convex functions, the agents' sum-utility, plus a nonsmooth (extended-valued) convex one. We propose a general unified algorithmic…

We present and analyze a stochastic distributed method (S-NEAR-DGD) that can tolerate inexact computation and inaccurate information exchange to alleviate the problems of costly gradient evaluations and bandwidth-limited communication in…

In this paper, we adopt a probability distribution estimation perspective to explore the optimization mechanisms of supervised classification using deep neural networks. We demonstrate that, when employing the Fenchel-Young loss, despite…

Gradient descent is the primary workhorse for optimizing large-scale problems in machine learning. However, its performance is highly sensitive to the choice of the learning rate. A key limitation of gradient descent is its lack of natural…

We present a unified framework to analyze the global convergence of Langevin dynamics based algorithms for nonconvex finite-sum optimization with $n$ component functions. At the core of our analysis is a direct analysis of the ergodicity of…

We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…

Gradient Descent Ascent (GDA) methods are the mainstream algorithms for minimax optimization in generative adversarial networks (GANs). Convergence properties of GDA have drawn significant interest in the recent literature. Specifically,…

We propose a novel linesearch variant of the trust region normal map-based semismooth Newton method developed in [Ouyang and Milzarek, Math. Program. 212(1-2), 389--435 (2025)] for solving a class of nonsmooth, nonconvex composite-type…