arXiv subjects

Thomas Parisini

Publications and source records attributed to Thomas Parisini.

At least 19 recordsLinked to original sources

arXiv2026

Communication-Efficient Distributed Learning with Differential Privacy

We address nonconvex learning problems over undirected networks. In particular, we focus on the challenge of designing an algorithm that is both communication-efficient and that guarantees the privacy of the agents' data. The first goal is achieved through a local training approach, which reduces communication frequency. The second goal is achieved by perturbing gradients during local training, specifically through gradient clipping and additive noise. We prove that the resulting algorithm converges to a stationary point of the problem within a bounded distance. Additionally, we provide theoretical privacy guarantees within a differential privacy framework that ensure agents' training data cannot be inferred from the trained model shared over the network. We show the algorithm's superior performance on a classification task under the same privacy budget, compared with state-of-the-art methods.

cs.LG↗

arXiv2026

A Functional Learning Approach for Team-Optimal Traffic Coordination

In this paper, we develop a kernel-based policy iteration functional learning framework for computing team-optimal strategies in traffic coordination problems. We consider a multi-agent discrete-time linear system with a cost function that combines quadratic regulation terms and nonlinear safety penalties. Building on the Hilbert space formulation of offline receding-horizon policy iteration, we seek approximate solutions within a reproducing kernel Hilbert space, where the policy improvement step is implemented via a discrete Fr\'echet derivative. We further study the model-free receding-horizon scenario, where the system dynamics are estimated using recursive least squares, followed by updating the policy using rolling online data. The proposed method is tested in signal-free intersection scenarios via both model-based and model-free simulations and validated in SUMO.

eess.SY↗

arXiv2026

Adaptive Mitigation of Insider Threats via Off-Policy Learning

An insider is a team member who covertly deviates from the team's optimal collaborative strategy to pursue a private objective while still appearing cooperative. Such an insider may initially behave cooperatively but later switch to selfish or malicious actions, thereby degrading collective performance, threatening mission success, and compromising operational safety. In this paper, we study such insider threats within an insider-aware, game-theoretic formulation, where the insider interacts with a decision maker (DM) under a continuous-time switched system, with each time interval characterized by a distinct insider behavioral pattern or threat level. We develop a periodic off-policy mitigation scheme that enables the DM to learn optimal mitigation policies from online data when encountering different insider threats, without requiring a priori knowledge of insider intentions. By designing appropriate conditions on the inter-learning interval time, we establish convergence guarantees for both the learning process and the closed-loop system, and characterize the corresponding mitigation performance achieved by the DM.

math.OC↗

arXiv2026

Distributed Unknown Input Observer Design: A Geometric Approach

We present a geometric approach to designing distributed unknown input observers (DUIOs) for linear time-invariant systems, where measurements are distributed across nodes and each node is influenced by \emph{unknown inputs} through distinct channels. The proposed distributed estimation scheme consists of a network of observers, each tasked with reconstructing the entire system state despite having access only to local input-output signals that are individually insufficient for full state observation. Unlike existing methods that impose stringent rank conditions on the input and output matrices at each node, our approach leverages the $(C,A)$-invariant (conditioned invariant) subspace at each node from a geometric perspective. This enables the design of DUIOs in both continuous- and discrete-time settings under relaxed conditions, for which we establish sufficiency and necessity. The effectiveness of our methodology is demonstrated through extensive simulations, including a practical case study on a power grid system.

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arXiv2025

Game-Theoretic Learning-Based Mitigation of Insider Threats

An insider is defined as a team member who covertly deviates from the team's optimal collaborative control strategy in pursuit of a private objective, while maintaining an outward appearance of cooperation. Such insider threats can severely undermine cooperative systems: subtle deviations may degrade collective performance, jeopardize mission success, and compromise operational safety. This paper presents a comprehensive framework for identifying and mitigating insider threats in cooperative control settings. We introduce an insider-aware, game-theoretic formulation in which the insider's hidden intention is parameterized, allowing the threat identification task to be reformulated as a parameter estimation problem. To address this challenge, we employ an online indirect dual adaptive control approach that simultaneously infers the insider's control strategy and counteracts its negative influence. By injecting properly designed probing signals, the resulting mitigation policy asymptotically recovers the nominal optimal control law - one that would be achieved under full knowledge of the insider's objective. Simulation results validate the effectiveness of the proposed identification-mitigation framework and illustrate its capability to preserve team performance even in the presence of covert adversarial behavior.

math.OC↗

arXiv2025

A Communication-Efficient Decentralized Actor-Critic Algorithm

In this paper, we study the problem of reinforcement learning in multi-agent systems where communication among agents is limited. We develop a decentralized actor-critic learning framework in which each agent performs several local updates of its policy and value function, where the latter is approximated by a multi-layer neural network, before exchanging information with its neighbors. This local training strategy substantially reduces the communication burden while maintaining coordination across the network. We establish finite-time convergence analysis for the algorithm under Markov-sampling. Specifically, to attain the $\varepsilon$-accurate stationary point, the sample complexity is of order $\mathcal{O}(\varepsilon^{-3})$ and the communication complexity is of order $\mathcal{O}(\varepsilon^{-1}\tau^{-1})$, where tau denotes the number of local training steps. We also show how the final error bound depends on the neural network's approximation quality. Numerical experiments in a cooperative control setting illustrate and validate the theoretical findings.

cs.LG↗

arXiv2025

Distributed Unknown Input Observer Design with Relaxed Conditions: Theory and Application to Vehicle Platooning

Designing observers for linear systems with both known and unknown inputs is an important problem in several research contexts, for example, fault diagnosis and fault-tolerant control, and cyber-secure control systems, and presents significant challenges in distributed state estimation due to the limited sensing capabilities of individual nodes. Existing methods typically impose an individual input-to-output rank condition on each estimator node, which severely restricts applicability in practical applications. This paper presents a novel distributed unknown-input observer design scheme based on a geometric approach under much weaker assumptions than the ones available in the literature. By leveraging the properties of the $(C, A)$-invariant (conditioned invariant) subspace at each node, our methodology aims at reconstructing portions of the system state that remain unaffected by local unknown inputs, while integrating these estimates via a network-based information exchange. A case study on vehicle platoon control shows the effectiveness of the proposed approach.

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arXiv2025

Jointly Computation- and Communication-Efficient Distributed Learning

We address distributed learning problems over undirected networks. Specifically, we focus on designing a novel ADMM-based algorithm that is jointly computation- and communication-efficient. Our design guarantees computational efficiency by allowing agents to use stochastic gradients during local training. Moreover, communication efficiency is achieved as follows: i) the agents perform multiple training epochs between communication rounds, and ii) compressed transmissions are used. We prove exact linear convergence of the algorithm in the strongly convex setting. We corroborate our theoretical results by numerical comparisons with state of the art techniques on a classification task.

cs.LG↗

arXiv2025

When Does Selfishness Align with Team Goals? A Structural Analysis of Equilibrium and Optimality

This paper investigates the relationship between the team-optimal solution and the Nash equilibrium (NE) to assess the impact of self-interested decisions on team performance. In classical team decision problems, team members typically act cooperatively towards a common objective to achieve a team-optimal solution. However, in practice, members may behave selfishly by prioritizing their goals, resulting in an NE under a non-cooperative game. To study this misalignment, we develop a parameterized model for team and game problems, where game parameters represent each individual's deviation from the team objective. The study begins by exploring the consistency and deviation between the NE and the team-optimal solution under fixed game parameters. We provide a necessary and sufficient condition for any NE to be a team optimum, along with establishing an upper bound to measure their difference when the consistency condition fails. The exploration then focuses on aligning NE strategies towards the team-optimal solution through the adjustment of game parameters, resulting in a non-convex and non-smooth bi-level optimization problem. We propose a hypergradient-based algorithm for this problem, and establish its convergence to the critical points. Finally, we validate our theoretical findings through extensive simulation studies.

math.OC↗

arXiv2025

Projected Gradient Descent for Constrained Decision-Dependent Optimization

This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected gradient descent (RPGD), which iteratively projects points onto evolving feasible sets throughout the optimization process. To analyze the impact of varying projection sets, we show a Lipschitz continuity property of projections onto varying sets with an explicitly given Lipschitz constant. Leveraging this property, we provide sufficient conditions for the convergence of RPGD to the constrained equilibrium point. Compared to the existing dual ascent method, RPGD ensures continuous feasibility throughout the optimization process and reduces the computational burden. We validate our results through numerical experiments on a market problem and dynamic pricing problem.

math.OC↗

arXiv2025

Data-Driven Adjustable Robust Optimization

In this paper, we develop a two-stage data-driven approach to address the adjustable robust optimization problem, where the uncertainty set is adjustable to manage infeasibility caused by significant or poorly quantified uncertainties. In the first stage, we synthesize an uncertainty set to ensure the feasibility of the problem as much as possible using the collected uncertainty samples. In the second stage, we find the optimal solution while ensuring that the constraints are satisfied under the new uncertainty set. This approach enlarges the feasible state set, at the expense of the risk of possible constraint violation. We analyze two scenarios: one where the uncertainty is non-stochastic, and another where the uncertainty is stochastic but with unknown probability distribution, leading to a distributionally robust optimization problem. In the first case, we scale the uncertainty set and find the best subset that fits the uncertainty samples. In the second case, we employ the Wasserstein metric to quantify uncertainty based on training data, and for polytope uncertainty sets, we further provide a finite program reformulation of the problem. The effectiveness of the proposed methods is demonstrated through an optimal power flow problem.

math.OC↗

arXiv2025

Fault Localisation in Infinite-Dimensional Linear Electrical Networks

We present a novel fault localisation methodology for linear time-invariant electrical networks with infinite-dimensional edge dynamics and uncertain fault dynamics. The theory accommodates instability and also bounded propagation delays in the network. The goal is to estimate the location of a fault along a given network edge, using sensors positioned arbitrarily throughout the network. Passive faults of unknown impedance are considered, along with stable faults of known impedance. To illustrate the approach, we tackle a significant use-case: a multi-conductor transmission line, with dynamics modelled by the Telegrapher's equation, subject to a line-to-ground fault. Frequency-domain insights are used to reformulate the general fault localisation problem into a non-convex scalar optimisation problem, of which the true fault location is guaranteed to be a global minimiser. Numerical experiments are run to quantify localisation performance over a range of fault resistances.

eess.SY↗

arXiv2025

Frequency-Domain Bounds for the Multiconductor Telegrapher's Equation

We establish mathematical bounds on the chain, ABCD and immittance matrices of a multiconductor transmission line, based on the Telegrapher's equation. Closed-form expressions for those matrices are also presented. Existing results that hold on the imaginary axis are extended to the complex plane, without reliance on a diagonalizability assumption that is prevalent in the literature. Therefore, the results remain valid under arbitrary arrangements of the conducting wires, which include electrical faults. The analysis ultimately reveals important system-theoretic implications of the Telegrapher's equation, which are of general relevance to control, power systems, and signal processing involving multiconductor transmission lines.

eess.SY↗

arXiv2025

Deviation Between Team-Optimal Solution and Nash Equilibrium in Flow Assignment Problems

We investigate the relationship between the team-optimal solution and the Nash equilibrium (NE) to assess the impact of strategy deviation on team performance. As a working use case, we focus on a class of flow assignment problems in which each source node acts as a cooperating decision maker (DM) within a team that minimizes the team cost based on the team-optimal strategy. In practice, some selfish DMs may prioritize their own marginal cost and deviate from NE strategies, thus potentially degrading the overall performance. To quantify this deviation, we explore the deviation bound between the team-optimal solution and the NE in two specific scenarios: (i) when the team-optimal solution is unique and (ii) when multiple solutions do exist. This helps DMs analyze the factors influencing the deviation and adopting the NE strategy within a tolerable range. Furthermore, in the special case of a potential game model, we establish the consistency between the team-optimal solution and the NE. Once the consistency condition is satisfied, the strategy deviation does not alter the total cost, and DMs do not face a strategic trade-off. Finally, we validate our theoretical analysis through some simulation studies.

cs.GT↗

arXiv2025

An exponentially stable discrete-time primal-dual algorithm for distributed constrained optimization

This paper studies a distributed algorithm for constrained consensus optimization that is obtained by fusing the Arrow-Hurwicz-Uzawa primal-dual gradient method for centralized constrained optimization and the Wang-Elia method for distributed unconstrained optimization. It is shown that the optimal primal-dual point is a semiglobally exponentially stable equilibrium for the algorithm, which implies linear convergence. The analysis is based on the separation between a slow centralized optimization dynamics describing the evolution of the average estimate toward the optimum, and a fast dynamics describing the evolution of the consensus error over the network. These two dynamics are mutually coupled, and the stability analysis builds on control theoretic tools such as time-scale separation, Lyapunov theory, and the small-gain principle. Our analysis approach highlights that the consensus dynamics can be seen as a fast, parasite one, and that stability of the distributed algorithm is obtained as a robustness consequence of the semiglobal exponential stability properties of the centralized method. This perspective can be used to enable other significant extensions, such as time-varying networks or delayed communication, that can be seen as ``perturbations" of the centralized algorithm.

math.OC↗

arXiv2025

Communication-Efficient Stochastic Distributed Learning

We address distributed learning problems, both nonconvex and convex, over undirected networks. In particular, we design a novel algorithm based on the distributed Alternating Direction Method of Multipliers (ADMM) to address the challenges of high communication costs, and large datasets. Our design tackles these challenges i) by enabling the agents to perform multiple local training steps between each round of communications; and ii) by allowing the agents to employ stochastic gradients while carrying out local computations. We show that the proposed algorithm converges to a neighborhood of a stationary point, for nonconvex problems, and of an optimal point, for convex problems. We also propose a variant of the algorithm to incorporate variance reduction thus achieving exact convergence. We show that the resulting algorithm indeed converges to a stationary (or optimal) point, and moreover that local training accelerates convergence. We thoroughly compare the proposed algorithms with the state of the art, both theoretically and through numerical results.

cs.LG↗

arXiv2025

Resilient Distributed Control for Uncertain Nonlinear Interconnected Systems under Network Anomaly

We address a distributed adaptive control methodology for nonlinear interconnected systems possibly affected by network anomalies. In the framework of adaptive approximation, the distributed controller and parameter estimator are designed by exploiting a backstepping approach. The stability of the distributed control system under anomalies is analyzed, where both local and neighboring anomaly effects are considered. To quantify the resilience of the interconnected system under the action of network anomalies, we derive bounds on the duration of each anomaly and the resting time between two consecutive anomalies. Specifically, when each anomaly duration is smaller than our designed upper bound, the interconnected system controlled by the distributed approximation-based controller remains asymptotically stable. Moreover, if the resting time between two consecutive anomalies is larger than the proposed bound, then all signals of the control system are guaranteed to be bounded. In the paper, we show that under the action of the proposed distributed adaptive controller, the interconnected system remains stable in the presence of network anomalies, with both the qualitative and quantitative resilient conditions. Extensive simulation results show the effectiveness of our theoretical results.

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arXiv2024

On the Output Redundancy of LTI Systems: A Geometric Approach with Application to Privacy

This paper examines the properties of output-redundant systems, that is, systems possessing a larger number of outputs than inputs, through the lenses of the geometric approach of Wonham et al. We begin by formulating a simple output allocation synthesis problem, which involves ``concealing" input information from a malicious eavesdropper having access to the system output, while still allowing for a legitimate user to reconstruct it. It is shown that the solvability of this problem requires the availability of a redundant set of outputs. This very problem is instrumental to unveiling the fundamental geometric properties of output-redundant systems, which form the basis for our subsequent constructions and results. As a direct application, we demonstrate how output allocation can be employed to effectively protect the information of input information from certain output eavesdroppers with guaranteed results.

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