Hierarchical Federated ADMM

In this paper, we depart from the widely-used gradient descent-based hierarchical federated learning (FL) algorithms to develop a novel hierarchical FL framework based on the alternating direction method of multipliers (ADMM). Within this framework, we propose two novel FL algorithms, which both use ADMM in the top layer: one that employs ADMM in the lower layer and another that uses the conventional gradient descent-based approach. The proposed framework enhances privacy, and experiments demonstrate the superiority of the proposed algorithms compared to the conventional algorithms in terms of learning convergence and accuracy. Additionally, gradient descent on the lower layer performs well even if the number of local steps is very limited, while ADMM on both layers lead to better performance otherwise.

Learning and Verifying Maximal Taylor-Neural Lyapunov functions

We introduce a novel neural network architecture, termed Taylor-neural Lyapunov functions, designed to approximate Lyapunov functions with formal certification. This architecture innovatively encodes local approximations and extends them globally by leveraging neural networks to approximate the residuals. Our method recasts the problem of estimating the largest region of attraction - specifically for maximal Lyapunov functions - into a learning problem, ensuring convergence around the origin through robust control theory. Physics-informed machine learning techniques further refine the estimation of the largest region of attraction. Remarkably, this method is versatile, operating effectively even without simulated data points. We validate the efficacy of our approach by providing numerical certificates of convergence across multiple examples. Our proposed methodology not only competes closely with state-of-the-art approaches, such as sum-of-squares and LyZNet, but also achieves comparable results even in the absence of simulated data. This work represents a significant advancement in control theory, with broad potential applications in the design of stable control systems and beyond.

A survey on secure decentralized optimization and learning

Decentralized optimization has become a standard paradigm for solving large-scale decision-making problems and training large machine learning models without centralizing data. However, this paradigm introduces new privacy and security risks, with malicious agents potentially able to infer private data or impair the model accuracy. Over the past decade, significant advancements have been made in developing secure decentralized optimization and learning frameworks and algorithms. This survey provides a comprehensive tutorial on these advancements. We begin with the fundamentals of decentralized optimization and learning, highlighting centralized aggregation and distributed consensus as key modules exposed to security risks in federated and distributed optimization, respectively. Next, we focus on privacy-preserving algorithms, detailing three cryptographic tools and their integration into decentralized optimization and learning systems. Additionally, we examine resilient algorithms, exploring the design and analysis of resilient aggregation and consensus protocols that support these systems. We conclude the survey by discussing current trends and potential future directions.

Energy Reduction in Cell-Free Massive MIMO through Fine-Grained Resource Management

The physical layer foundations of cell-free massive MIMO (CF-mMIMO) have been well-established. As a next step, researchers are investigating practical and energy-efficient network implementations. This paper focuses on multiple sets of access points (APs) where user equipments (UEs) are served in each set, termed a federation, without inter-federation interference. The combination of federations and CF-mMIMO shows promise for highly-loaded scenarios. Our aim is to minimize the total energy consumption while adhering to UE downlink data rate constraints. The energy expenditure of the full system is modelled using a detailed hardware model of the APs. We jointly design the AP-UE association variables, determine active APs, and assign APs and UEs to federations. To solve this highly combinatorial problem, we develop a novel alternating optimization algorithm. Simulation results for an indoor factory demonstrate the advantages of considering multiple federations, particularly when facing large data rate requirements. Furthermore, we show that adopting a more distributed CF-mMIMO architecture is necessary to meet the data rate requirements. Conversely, if feasible, using a less distributed system with more antennas at each AP is more advantageous from an energy savings perspective.

Enhancing Privacy in Federated Learning through Local Training

In this paper we propose the federated private local training algorithm (Fed-PLT) for federated learning, to overcome the challenges of (i) expensive communications and (ii) privacy preservation. We address (i) by allowing for both partial participation and local training, which significantly reduce the number of communication rounds between the central coordinator and computing agents. The algorithm matches the state of the art in the sense that the use of local training demonstrably does not impact accuracy. Additionally, agents have the flexibility to choose from various local training solvers, such as (stochastic) gradient descent and accelerated gradient descent. Further, we investigate how employing local training can enhance privacy, addressing point (ii). In particular, we derive differential privacy bounds and highlight their dependence on the number of local training epochs. We assess the effectiveness of the proposed algorithm by comparing it to alternative techniques, considering both theoretical analysis and numerical results from a classification task.

Online Distributed Learning over Random Networks

The recent deployment of multi-agent systems in a wide range of scenarios has enabled the solution of learning problems in a distributed fashion. In this context, agents are tasked with collecting local data and then cooperatively train a model, without directly sharing the data. While distributed learning offers the advantage of preserving agents' privacy, it also poses several challenges in terms of designing and analyzing suitable algorithms. This work focuses specifically on the following challenges motivated by practical implementation: (i) online learning, where the local data change over time; (ii) asynchronous agent computations; (iii) unreliable and limited communications; and (iv) inexact local computations. To tackle these challenges, we introduce the Distributed Operator Theoretical (DOT) version of the Alternating Direction Method of Multipliers (ADMM), which we call the DOT-ADMM Algorithm. We prove that it converges with a linear rate for a large class of convex learning problems (e.g., linear and logistic regression problems) toward a bounded neighborhood of the optimal time-varying solution, and characterize how the neighborhood depends on~$\text{(i)--(iv)}$. We corroborate the theoretical analysis with numerical simulations comparing the DOT-ADMM Algorithm with other state-of-the-art algorithms, showing that only the proposed algorithm exhibits robustness to (i)--(iv).

Online Distributed Learning with Quantized Finite-Time Coordination

In this paper we consider online distributed learning problems. Online distributed learning refers to the process of training learning models on distributed data sources. In our setting a set of agents need to cooperatively train a learning model from streaming data. Differently from federated learning, the proposed approach does not rely on a central server but only on peer-to-peer communications among the agents. This approach is often used in scenarios where data cannot be moved to a centralized location due to privacy, security, or cost reasons. In order to overcome the absence of a central server, we propose a distributed algorithm that relies on a quantized, finite-time coordination protocol to aggregate the locally trained models. Furthermore, our algorithm allows for the use of stochastic gradients during local training. Stochastic gradients are computed using a randomly sampled subset of the local training data, which makes the proposed algorithm more efficient and scalable than traditional gradient descent. In our paper, we analyze the performance of the proposed algorithm in terms of the mean distance from the online solution. Finally, we present numerical results for a logistic regression task.

OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regression

This paper presents a new regularization approach -- termed OpReg-Boost -- to boost the convergence and lessen the asymptotic error of online optimization and learning algorithms. In particular, the paper considers online algorithms for optimization problems with a time-varying (weakly) convex composite cost. For a given online algorithm, OpReg-Boost learns the closest algorithmic map that yields linear convergence; to this end, the learning procedure hinges on the concept of operator regression. We show how to formalize the operator regression problem and propose a computationally-efficient Peaceman-Rachford solver that exploits a closed-form solution of simple quadratically-constrained quadratic programs (QCQPs). Simulation results showcase the superior properties of OpReg-Boost w.r.t. the more classical forward-backward algorithm, FISTA, and Anderson acceleration, and with respect to its close relative convex-regression-boost (CvxReg-Boost) which is also novel but less performing.

tvopt: A Python Framework for Time-Varying Optimization

This paper introduces tvopt, a Python framework for prototyping and benchmarking time-varying (or online) optimization algorithms. The paper first describes the theoretical approach that informed the development of tvopt. Then it discusses the different components of the framework and their use for modeling and solving time-varying optimization problems. In particular, tvopt provides functionalities for defining both centralized and distributed online problems, and a collection of built-in algorithms to solve them, for example gradient-based methods, ADMM and other splitting methods. Moreover, the framework implements prediction strategies to improve the accuracy of the online solvers. The paper then proposes some numerical results on a benchmark problem and discusses their implementation using tvopt. The code for tvopt is available at https://github.com/nicola-bastianello/tvopt.

Primal and Dual Prediction-Correction Methods for Time-Varying Convex Optimization

We propose a unified framework for time-varying convex optimization based on the prediction-correction paradigm, both in the primal and dual spaces. In this framework, a continuously varying optimization problem is sampled at fixed intervals, and each problem is approximately solved with a primal or dual correction step. The solution method is warm-started with the output of a prediction step, which solves an approximation of a future problem using past information. Prediction approaches are studied and compared under different sets of assumptions. Examples of algorithms covered by this framework are time-varying versions of the gradient method, splitting methods, and the celebrated alternating direction method of multipliers (ADMM).