Matrix completion is fundamental for predicting missing data with a wide range of applications in personalized healthcare, e-commerce, recommendation systems, and social network analysis. Traditional matrix completion approaches typically assume centralized data storage, which raises challenges in terms of computational efficiency, scalability, and user privacy. In this paper, we address the problem of federated matrix completion, focusing on scenarios where user-specific data is distributed across multiple clients, and privacy constraints are uncompromising. Federated learning provides a promising framework to address these challenges by enabling collaborative learning across distributed datasets without sharing raw data. We propose \texttt{FedMC-ADMM} for solving federated matrix completion problems, a novel algorithmic framework that combines the Alternating Direction Method of Multipliers with a randomized block-coordinate strategy and alternating proximal gradient steps. Unlike existing federated approaches, \texttt{FedMC-ADMM} effectively handles multi-block 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 matrix completion in the presence of multi-block variables. To validate our approach, we conduct extensive experiments on real-world datasets, including MovieLens 1M, 10M, and Netflix. The results demonstrate that \texttt{FedMC-ADMM} outperforms existing methods in terms of convergence speed and testing accuracy.

Additive Manufacturing (AM) is transforming the manufacturing sector by enabling efficient production of intricately designed products and small-batch components. However, metal parts produced via AM can include flaws that cause inferior mechanical properties, including reduced fatigue response, yield strength, and fracture toughness. To address this issue, we leverage convolutional neural networks (CNN) to analyze thermal images of printed layers, automatically identifying anomalies that impact these properties. We also investigate various synthetic data generation techniques to address limited and imbalanced AM training data. Our models' defect detection capabilities were assessed using images of Nickel alloy 718 layers produced on a laser powder bed fusion AM machine and synthetic datasets with and without added noise. Our results show significant accuracy improvements with synthetic data, emphasizing the importance of expanding training sets for reliable defect detection. Specifically, Generative Adversarial Networks (GAN)-generated datasets streamlined data preparation by eliminating human intervention while maintaining high performance, thereby enhancing defect detection capabilities. Additionally, our denoising approach effectively improves image quality, ensuring reliable defect detection. Finally, our work integrates these models in the CLoud ADditive MAnufacturing (CLADMA) module, a user-friendly interface, to enhance their accessibility and practicality for AM applications. This integration supports broader adoption and practical implementation of advanced defect detection in AM processes.

Developing effective Multi-Agent Systems (MAS) is critical for many applications requiring collaboration and coordination with humans. Despite the rapid advance of Multi-Agent Deep Reinforcement Learning (MADRL) in cooperative MAS, one major challenge 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 nonstationary environments that require coordination among people. In this paper, 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 (MAIBL). The idea of these MAIBL algorithms is to combine the cognitive mechanisms of IBLT and the techniques of MADRL models to deal with coordination MAS 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 paper, we introduce TITAN, a novel inerTIal block majorizaTion minimizAtioN framework for non-smooth non-convex 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.

In this paper, we propose an algorithmic framework, dubbed inertial alternating direction methods of multipliers (iADMM), for solving a class of nonconvex nonsmooth multiblock composite optimization problems with linear constraints. Our framework employs the general minimization-majorization (MM) principle to update each block of variables so as to not only unify the convergence analysis of previous ADMM that use specific surrogate functions in the MM step, but also lead to new efficient ADMM schemes. To the best of our knowledge, in the nonconvex nonsmooth setting, ADMM used in combination with the MM principle to update each block of variables, and ADMM combined with \emph{inertial terms for the primal variables} have not been studied in the literature. Under standard assumptions, we prove the subsequential convergence and global convergence for the generated sequence of iterates. We illustrate the effectiveness of iADMM on a class of nonconvex low-rank representation problems.

In this paper, we consider a class of nonsmooth nonconvex optimization problems whose objective is the sum of a block relative smooth function and a proper and lower semicontinuous block separable function. Although the analysis of block proximal gradient (BPG) methods for the class of block $L$-smooth functions have been successfully extended to Bregman BPG methods that deal with the class of block relative smooth functions, accelerated Bregman BPG methods are scarce and challenging to design. Taking our inspiration from Nesterov-type acceleration and the majorization-minimization scheme, we propose a block alternating Bregman Majorization-Minimization framework with Extrapolation (BMME). We prove subsequential convergence of BMME to a first-order stationary point under mild assumptions, and study its global convergence under stronger conditions. We illustrate the effectiveness of BMME on the penalized orthogonal nonnegative matrix factorization problem.