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Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton…

This paper addresses a distributed optimization problem in a communication network where nodes are active sporadically. Each active node applies some learning method to control its action to maximize the global utility function, which is…

Data-driven inverse optimization for mixed-integer linear programs (MILPs), which seeks to learn an objective function and constraints consistent with observed decisions, is important for building accurate mathematical models in a variety…

Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…

Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is…

Learning to Optimize (LtO) is a problem setting in which a machine learning (ML) model is trained to emulate a constrained optimization solver. Learning to produce optimal and feasible solutions subject to complex constraints is a difficult…

In this letter, an accelerated quadratic programming (QP) algorithm is proposed based on the proximal gradient method. The algorithm can achieve convergence rate $O(1/p^{\alpha})$, where $p$ is the iteration number and $\alpha$ is the given…

The continuous dynamical system approach to deep learning is explored in order to devise alternative frameworks for training algorithms. Training is recast as a control problem and this allows us to formulate necessary optimality conditions…

In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…

Optimization is an integral part of modern deep learning. Recently, the concept of learned optimizers has emerged as a way to accelerate this optimization process by replacing traditional, hand-crafted algorithms with meta-learned…

We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal $\pm$ rank-$r$ symmetric positive definite matrices. This special type of metric allows for a…

Distance metric learning is successful in discovering intrinsic relations in data. However, most algorithms are computationally demanding when the problem size becomes large. In this paper, we propose a discriminative metric learning…

Recent years have seen considerable progress in the continual training of deep neural networks, predominantly thanks to approaches that add replay or regularization terms to the loss function to approximate the joint loss over all tasks so…

The distributed optimization problem has become increasingly relevant recently. It has a lot of advantages such as processing a large amount of data in less time compared to non-distributed methods. However, most distributed approaches…

Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…

Distributed optimization and learning algorithms are designed to operate over large scale networks enabling processing of vast amounts of data effectively and efficiently. One of the main challenges for ensuring a smooth learning process in…

The training phase is the most important stage during the machine learning process. In the case of labeled data and supervised learning, machine training consists in minimizing the loss function subject to different constraints. In an…

By exploiting the correlation between the structure and the solution of Mixed-Integer Linear Programming (MILP), Machine Learning (ML) has become a promising method for solving large-scale MILP problems. Existing ML-based MILP solvers…

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…