Matrix completion (MC) is fundamental for predicting missing data with a wide range of applications in personalized healthcare, e-commerce, recommendation systems, and social network analysis. Traditional MC approaches typically assume centralized data storage, which raises challenges in terms of computational efficiency, scalability, and user privacy. In this article, we address the problem of federated MC, focusing on scenarios where user-specific data is distributed across multiple clients, and privacy constraints are uncompromising. Federated learning (FL) provides a promising framework to address these challenges by enabling collaborative learning across distributed datasets without sharing raw data. We propose FedMC-ADMM for solving federated MC problems, a novel algorithmic framework that combines the alternating direction method of multipliers (ADMM) with a randomized block-coordinate strategy and alternating proximal gradient steps. Unlike existing federated approaches, FedMC-ADMM effectively handles multiblock nonconvex and nonsmooth optimization problems, allowing efficient computation while preserving user privacy. We analyze the theoretical properties of our algorithm, demonstrating subsequential convergence and establishing a convergence rate of $\mathcal {O}(K^{-1/2})$ , leading to a communication complexity of $\mathcal {O}(\epsilon ^{-2})$ for reaching an $\epsilon $ -stationary point. This work is the first to establish these theoretical guarantees for federated MC in the presence of multiblock variables. To validate our approach, we conduct extensive experiments on real-world datasets, including MovieLens 1M, 10M, and Netflix. The results demonstrate that FedMC-ADMM outperforms existing methods in terms of convergence speed and testing accuracy.

Boolean Matrix Factorization (BMF) is a widely used technique to model binary interaction data in applications such as recommender systems, bioinformatics, and pattern mining. It approximates a binary matrix as the Boolean product of two low-rank binary matrices, capturing latent structure while preserving interpretability. While most existing work on BMF focuses on centralized settings, in real-world scenarios data is often distributed across clients due to privacy concerns. Federated BMF addresses this by enabling collaborative learning without sharing raw data. However, existing federated factorization methods are designed for real-valued or non-negative data and are ill-suited for Boolean structures. These methods either fail to preserve binary constraints or rely on relaxations that produce approximate outputs without guarantees. We address this by proposing a federated BMF algorithm based on alternating optimization combined with a randomized block-coordinate strategy. Each subproblem is solved exactly via integer programming, and the algorithm does not require all clients to participate in every communication round. Experiments on benchmark datasets for cancer genomics and recommendation tasks show that our method outperforms existing baselines by achieving lower prediction and reconstruction errors.

In this paper, we introduce TITAN, a novel inerTIal block majorizaTion minimizAtioN ramework for nonsmooth nonconvex optimization problems. To the best of our knowledge, TITAN is the first framework of block-coordinate update method that relies on the majorization-minimization framework while embedding inertial force to each step of the block updates. The inertial force is obtained via an extrapolation operator that subsumes heavy-ball and Nesterov-type accelerations for block proximal gradient methods as special cases. By choosing various surrogate functions, such as proximal, Lipschitz gradient, Bregman, quadratic, and composite surrogate functions, and by varying the extrapolation operator, TITAN produces a rich set of inertial block-coordinate update methods. We study sub-sequential convergence as well as global convergence for the generated sequence of TITAN. We illustrate the effectiveness of TITAN on two important machine learning problems, namely sparse non-negative matrix factorization and matrix completion.

Developing effective multi-agent systems (MASs) is critical for many applications requiring collaboration and coordination with humans. Despite the rapid advance of multi-agent deep reinforcement learning (MADRL) in cooperative MASs, one of the major challenges that remain is the simultaneous learning and interaction of independent agents in dynamic environments in the presence of stochastic rewards. State-of-the-art MADRL models struggle to perform well in Coordinated Multi-agent Object Transportation Problems (CMOTPs) wherein agents must coordinate with each other and learn from stochastic rewards. In contrast, humans often learn rapidly to adapt to non-stationary environments that require coordination among people. In this article, motivated by the demonstrated ability of cognitive models based on Instance-based Learning Theory (IBLT) to capture human decisions in many dynamic decision-making tasks, we propose three variants of multi-agent IBL models (MAIBLs). The idea of these MAIBL algorithms is to combine the cognitive mechanisms of IBLT and the techniques of MADRL models to deal with coordination MASs in stochastic environments from the perspective of independent learners. We demonstrate that the MAIBL models exhibit faster learning and achieve better coordination in a dynamic CMOTP task with various settings of stochastic rewards compared to current MADRL models. We discuss the benefits of integrating cognitive insights into MADRL models.

In this work, we present a variant of DCA (Difference of Convex function Algorithm) with the aim to improve its convergence speed. The proposed algorithm, named Accelerated DCA (ADCA), consists in incorporating the Nesterov's acceleration technique into DCA. We first investigate ADCA for solving the standard DC program and rigorously study its convergence properties and the convergence rate. Secondly, we develop ADCA for a special case of the standard DC program whose the objective function is the sum of a differentiable with L-Lipschitz gradient function (possibly nonconvex) and a nonsmooth DC function. We exploit the special structure of the problem to propose an efficient DC decomposition for which the corresponding ADCA scheme is inexpensive. As an application, we consider the sparse binary logistic regression problem. Numerical experiments on several benchmark datasets illustrate the efficiency of our algorithm and its superiority over well-known methods.

We present a novel approach for estimating multiple sparse precision matrices using the ℓ0,0regularization. The multiple precision matrices share some common structures such as the weights or locations of non-zero elements, we are interested in selecting simultaneously elements on each precision matrix as well as across multiple precision matrices. This is referred as bi-level variable selection. The optimization problem can be formulated as DC (Difference of Convex functions) programs to which DC programming and DCA (DC Algorithm) are investigated. The experimental results on both simulated and real datasets demonstrate the efficiency of our algorithms.

In this paper, we present a stochastic version of DCA (Difference of Convex functions Algorithm) to solve a class of optimization problems whose objective function is a large sum of non-convex functions and a regularization term. We consider the $\ell_{2,0}$ regularization to deal with the group variables selection. By exploiting the special structure of the problem, we propose an efficient DC decomposition for which the corresponding stochastic DCA scheme is very inexpensive: it only requires the projection of points onto balls that is explicitly computed. As an application, we applied our algorithm for the group variables selection in multiclass logistic regression. Numerical experiments on several benchmark datasets and synthetic datasets illustrate the efficiency of our algorithm and its superiority over well-known methods, with respect to classification accuracy, sparsity of solution as well as running time.

This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The objective function of SCME problem is composed of a nonconvex part and the [Formula: see text] term, which is discontinuous and difficult to tackle. Appropriate DC (difference of convex functions) approximations of [Formula: see text]-norm are used that result in approximation SCME problems that are still nonconvex. DC programming and DCA (DC algorithm), powerful tools in nonconvex programming framework, are investigated. Two DC formulations are proposed and corresponding DCA schemes developed. Two applications of the SCME problem that are considered are classification via sparse quadratic discriminant analysis and portfolio optimization. A careful empirical experiment is performed through simulated and real data sets to study the performance of the proposed algorithms. Numerical results showed their efficiency and their superiority compared with seven state-of-the-art methods.