In this paper we focus on the solution of online problems with time-varying, linear equality and inequality constraints. Our approach is to design a novel online algorithm by leveraging the tools of control theory. In particular, for the case of equality constraints only, using robust control we design an online algorithm with asymptotic convergence to the optimal trajectory, differently from the alternatives that achieve non-zero tracking error. When also inequality constraints are present, we show how to modify the proposed algorithm to account for the wind-up induced by the nonnegativity constraints on the dual variables. We report numerical results that corroborate the theoretical analysis, and show how the proposed approach outperforms state-of-the-art algorithms both with equality and inequality constraints.

In this letter, 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), leveraging a network architecture consisting of a single cloud server and multiple edge servers, where each edge server is dedicated to a specific client set. 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.

The recent deployment of multiagent networks has enabled the distributed solution of learning problems, where agents cooperate to train a global model without sharing their local, private data. This work specifically targets some prevalent challenges inherent to distributed learning: 1) online training, i.e., the local data change over time; 2) asynchronous agent computations; 3) unreliable and limited communications; and 4) inexact local computations. To tackle these challenges, we apply the distributed operator theoretical (DOT) version of the alternating direction method of multipliers (ADMM), which we call "DOT-ADMM." We prove that if the DOT-ADMM operator is metric subregular, then it converges with a linear rate for a large class of (not necessarily strongly) convex learning problems toward a bounded neighborhood of the optimal time-varying solution, and characterize how such neighborhood depends on 1)-4). We first derive an easy-to-verify condition for ensuring the metric subregularity of an operator, followed by tutorial examples on linear and logistic regression problems. We corroborate the theoretical analysis with numerical simulations comparing DOT-ADMM with other state-of-the-art algorithms, showing that only the proposed algorithm exhibits robustness to 1)-4).

In this paper we address distributed learning problems over peer-to-peer networks. In particular, we focus on the challenges of quantized communications, asynchrony, and stochastic gradients that arise in this set-up. We first discuss how to turn the presence of quantized communications into an advantage, by resorting to a finite-time, quantized coordination scheme. This scheme is combined with a distributed gradient descent method to derive the proposed algorithm. Secondly, we show how this algorithm can be adapted to allow asynchronous operations of the agents, as well as the use of stochastic gradients. Finally, we propose a variant of the algorithm which employs zooming-in quantization. We analyze the convergence of the proposed methods and compare them to state-of-the-art alternatives.

In this paper, we focus on distributed learning over peer-to-peer networks. In particular, we address the challenge of expensive communications (which arise when e.g. training neural networks), by proposing a novel local training algorithm, LTADMM. We extend the distributed ADMM enabling the agents to perform multiple local gradient steps per communication round (local training). We present a preliminary convergence analysis of the algorithm under a graph regularity assumption, and show how the use of local training does not compromise the accuracy of the learned model. We compare the algorithm with the state of the art for a classification task, and in different set-ups. The results are very promising showing a great performance of LT-ADMM, and paving the way for future important theoretical developments.

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.

In this article, we propose a model-based approach to the design of online optimization algorithms, with the goal of improving the tracking of the solution trajectory (trajectories) w.r.t. state-of-the-art methods. We focus first on quadratic problems with a time-varying linear term, and use digital control tools (a robust internal model principle) to propose a novel online algorithm that can achieve zero tracking error by modeling the cost with a dynamical system. We prove the convergence of the algorithm for both strongly convex and convex problems. We further discuss the sensitivity of the proposed method to model uncertainties and quantify its performance. We discuss how the proposed algorithm can be applied to general (nonquadratic) problems using an approximate model of the cost, and analyze the convergence leveraging the small gain theorem. We present numerical results that showcase the superior performance of the proposed algorithms over previous methods for both quadratic and nonquadratic problems.

In this paper, we address the problem of detecting anomalies in the reaction wheel assemblies (RWAs) of a satellite. These anomalies can alert of an impending failure in a RWA, and effective detection would allow to take preventive action. To this end, we propose a novel algorithm that detects and categorizes anomalies in the friction profile of an RWA, where the profile relates spin rate to measured friction torque. The algorithm, developed in a probabilistic framework, runs in real-time and has a tunable false positive rate as a parameter. The performance of the proposed method is thoroughly tested in a number of numerical experiments, with different anomalies of varying severity.

This manuscript proposes novel distributed algorithms for solving the dynamic consensus problem in discrete-time multi-agent systems on three different objective functions: the average, the maximum, and the median. In this problem, each agent has access to an external time-varying scalar signal and aims to estimate and track a function of all the signals by exploiting only local communications with other agents. By recasting the problem as an online distributed optimization problem, the proposed algorithms are derived based on the distributed implementation of the alternating direction method of multipliers (ADMM) and are thus amenable to a unified analysis technique. A major contribution is that of proving linear convergence of these ADMM-based algorithms for the specific dynamic consensus problems of interest, for which current results could only guarantee sub-linear convergence. In particular, the tracking error is shown to converge within a bound, whereas the steady-state error is zero. Numerical simulations corroborate the theoretical findings, empirically show the robustness of the proposed algorithms to re-initialization errors, and compare their performance with that of state-of-the-art algorithms.

In this paper, we propose a novel distributed algorithm for consensus optimization over networks. The key idea is to achieve dynamic consensus on the agents' average and on the global descent direction by iteratively solving an online auxiliary optimization problem through the Alternating Direction Method of Multipliers (ADMM). Such a mechanism is suitably interlaced with a local proportional action steering each agent estimate to the solution of the original consensus optimization problem. The analysis uses tools from system theory to prove the linear convergence of the scheme with strongly convex costs. Finally, some numerical simulations confirm our findings and show the robustness of the proposed scheme.