Related papers: Unrolled Graph Neural Networks for Constrained Opt…

In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…

A fundamental challenge for machine learning models is generalizing to out-of-distribution (OOD) data, in part due to spurious correlations. To tackle this challenge, we first formalize the OOD generalization problem as constrained…

In this work, we propose to employ information-geometric tools to optimize a graph neural network architecture such as the graph convolutional networks. More specifically, we develop optimization algorithms for the graph-based…

This paper analyzes the contraction of the primal-dual gradient optimization via contraction theory in the context of discrete-time updating dynamics. The contraction theory based on Riemannian manifolds is first established for convergence…

While Annealing Machines (AM) have shown increasing capabilities in solving complex combinatorial problems, positioning themselves as a more immediate alternative to the expected advances of future fully quantum solutions, there are still…

Graph Neural Networks (GNNs) have achieved impressive performance in graph-related tasks. However, they suffer from poor generalization on out-of-distribution (OOD) data, as they tend to learn spurious correlations. Such correlations…

Distributed optimization is an important direction of research in modern optimization theory. Its applications include large scale machine learning, distributed signal processing and many others. The paper studies decentralized min-max…

This paper studies a distributed online convex optimization problem, where agents in an unbalanced network cooperatively minimize the sum of their time-varying local cost functions subject to a coupled inequality constraint. To solve this…

We develop an efficient method for solving non-convex constrained optimization problems that are pervasive in economics. The optimal solution to these problems often involves randomization. We employ a Lagrangian framework and prove that…

We consider regression problems with binary weights. Such optimization problems are ubiquitous in quantized learning models and digital communication systems. A natural approach is to optimize the corresponding Lagrangian using variants of…

Graph signal processing is a ubiquitous task in many applications such as sensor, social, transportation and brain networks, point cloud processing, and graph neural networks. Often, graph signals are corrupted in the sensing process, thus…

We consider the broad class of decentralized optimal resource allocation problems in wireless networks, which can be formulated as a constrained statistical learning problems with a localized information structure. We develop the use of…

Mathematical optimization is the workhorse behind several aspects of modern robotics and control. In these applications, the focus is on constrained optimization, and the ability to work on manifolds (such as the classical matrix Lie…

In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…

In recent studies, several asymptotic upper bounds on generalization errors on deep neural networks (DNNs) are theoretically derived. These bounds are functions of several norms of weights of the DNNs, such as the Frobenius and spectral…

Deep neural networks (DNNs) have achieved remarkable success in computer vision; however, training DNNs for satisfactory performance remains challenging and suffers from sensitivity to empirical selections of an optimization algorithm for…

In this paper, we present a learning method to solve the unlabelled motion problem with motion constraints and space constraints in 2D space for a large number of robots. To solve the problem of arbitrary dynamics and constraints we propose…

This paper considers smooth convex optimization problems with many functional constraints. To solve this general class of problems we propose a new stochastic perturbed augmented Lagrangian method, called SGDPA, where a perturbation is…

This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are…

Training of neural networks amounts to nonconvex optimization problems that are typically solved by using backpropagation and (variants of) stochastic gradient descent. In this work we propose an alternative approach by viewing the training…