This paper proposes a novel approach to resilient distributed optimization with quadratic costs in a networked control system (e.g., wireless sensor network, power grid, robotic team) prone to external attacks (e.g., hacking, power outage) that cause agents to misbehave. Departing from classical filtering strategies proposed in literature, we draw inspiration from a game-theoretic formulation of the consensus problem and argue that adding competition to the mix can enhance resilience in the presence of malicious agents. Our intuition is corroborated by analytical and numerical results showing that i) our strategy highlights the presence of a nontrivial tradeoff between blind collaboration and full competition, and ii) such competition-based approach can outperform state-of-the-art algorithms based on Mean Subsequence Reduced.

There is a growing interest in the decentralized optimization framework that goes under the name of Federated Learning (FL). In particular, much attention is being turned to FL scenarios where the network is strongly heterogeneous in terms of communication resources (e.g., bandwidth) and data distribution. In these cases, communication between local machines (agents) and the central server (Master) is a main consideration. In this work, we present an original communication-constrained Newton-type (NT) algorithm designed to accelerate FL in such heterogeneous scenarios. The algorithm is by design robust to non i.i.d. data distributions, handles heterogeneity of agents' communication resources (CRs), only requires sporadic Hessian computations, and achieves super-linear convergence. This is possible thanks to an incremental strategy, based on a singular value decomposition (SVD) of the local Hessian matrices, which exploits (possibly) outdated second-order information. The proposed solution is thoroughly validated on real datasets by assessing (i) the number of communication rounds required for convergence, (ii) the overall amount of data transmitted and (iii) the number of local Hessian computations required. For all these metrics, the proposed approach shows superior performance against state-of-the art techniques like GIANT and FedNL.

This paper investigates the use of a networked system ($e.g.$, swarm of robots, smart grid, sensor network) to monitor a time-varying phenomenon of interest in the presence of communication and computation latency. Recent advances in edge computing have enabled processing to be spread across the network, hence we investigate the fundamental computation-communication trade-off, arising when a sensor has to decide whether to transmit raw data (incurring communication delay) or preprocess them (incurring computational delay) in order to compute an accurate estimate of the state of the phenomenon of interest. We propose two key contributions. First, we formalize the notion of $processing$ $network$. Contrarily to $sensor$ $and$ $communication$ $networks$, where the designer is concerned with the design of a suitable communication policy, in a processing network one can also control when and where the computation occurs in the network. The second contribution is to provide analytical results on the optimal preprocessing delay ($i.e.$, the optimal time spent on computations at each sensor) for the case with a single sensor and multiple homogeneous sensors. Numerical results substantiate our claims that accounting for computation latencies (both at sensor and estimator side) and communication delays can largely impact the estimation accuracy.

In this work we study the non-parametric reconstruction of spatio-temporal dynamical Gaussian processes (GPs) via GP regression from sparse and noisy data. GPs have been mainly applied to spatial regression where they represent one of the most powerful estimation approaches also thanks to their universal representing properties. Their extension to dynamical processes has been instead elusive so far since classical implementations lead to unscalable algorithms. We then propose a novel procedure to address this problem by coupling GP regression and Kalman filtering. In particular, assuming space/time separability of the covariance (kernel) of the process and rational time spectrum, we build a finite-dimensional discrete-time state-space process representation amenable of Kalman filtering. With sampling over a finite set of fixed spatial locations, our major finding is that the Kalman filter state at instant $t_k$ represents a sufficient statistic to compute the minimum variance estimate of the process at any $t \geq t_k$ over the entire spatial domain. This result can be interpreted as a novel Kalman representer theorem for dynamical GPs. We then extend the study to situations where the set of spatial input locations can vary over time. The proposed algorithms are finally tested on both synthetic and real field data, also providing comparisons with standard GP and truncated GP regression techniques.

We consider a scenario where the aim of a group of agents is to perform the optimal coverage of a region according to a sensory function. In particular, centroidal Voronoi partitions have to be computed. The difficulty of the task is that the sensory function is unknown and has to be reconstructed on line from noisy measurements. Hence, estimation and coverage needs to be performed at the same time. We cast the problem in a Bayesian regression framework, where the sensory function is seen as a Gaussian random field. Then, we design a set of control inputs which try to well balance coverage and estimation, also discussing convergence properties of the algorithm. Numerical experiments show the effectivness of the new approach.