arXiv subjects

Filippo Fabiani

Publications and source records attributed to Filippo Fabiani.

At least 19 recordsLinked to original sources

arXiv2026

Generalization as a robust performance property of learning-enabled dynamical systems

By focusing on algorithmic stability as a means of establishing out-of-sample bounds, we provide a system-theoretic interpretation of generalization in learning-enabled dynamical systems arising in data-driven optimization and feedback control approximation. Given two neighboring datasets, we specifically model sample replacement as an exogenous disturbance acting on a sensitivity system, while the incremental behavior of the data-dependent operator is encoded through an integral quadratic constraint. By relying on dissipativity arguments, we establish a matrix inequality-based certificate and a uniform stability bound that separates the one-sample sensitivity of the learned operator, and an algorithm-dependent dynamical gain. The latter can then be optimized, offering a tractable tool for certifying and comparing generalization capabilities of learning dynamics. We show that our results recover classical ones for gradient descent, apply naturally to momentum-based methods such as heavy-ball and Nesterov acceleration, and extend to data-driven control.

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arXiv2025

Finite-sample guarantees for data-driven forward-backward operator methods

We establish finite sample certificates on the quality of solutions produced by data-based forward-backward (FB) operator splitting schemes. As frequently happens in stochastic regimes, we consider the problem of finding a zero of the sum of two operators, where one is either unavailable in closed form or computationally expensive to evaluate, and shall therefore be approximated using a finite number of noisy oracle samples. Under the lens of algorithmic stability, we then derive probabilistic bounds on the distance between a true zero and the FB output without making specific assumptions about the underlying data distribution. We show that under weaker conditions ensuring the convergence of FB schemes, stability bounds grow proportionally to the number of iterations. Conversely, stronger assumptions yield stability guarantees that are independent of the iteration count. We then specialize our results to a popular FB stochastic Nash equilibrium seeking algorithm and validate our theoretical bounds on a control problem for smart grids, where the energy price uncertainty is approximated by means of historical data.

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arXiv2025

Concentration inequalities for semidefinite least squares based on data

We study data-driven least squares (LS) problems with semidefinite (SD) constraints and derive finite-sample guarantees on the spectrum of their optimal solutions when these constraints are relaxed. In particular, we provide a high confidence bound allowing one to solve a simpler program in place of the full SDLS problem, while ensuring that the eigenvalues of the resulting solution are $\varepsilon$-close of those enforced by the SD constraints. The developed certificate, which consistently shrinks as the number of data increases, turns out to be easy-to-compute, distribution-free, and only requires independent and identically distributed samples. Moreover, when the SDLS is used to learn an unknown quadratic function, we establish bounds on the error between a gradient descent iterate minimizing the surrogate cost obtained with no SD constraints and the true minimizer.

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arXiv2025

Distributed equilibrium seeking in aggregative games: linear convergence under singular perturbations lens

We present a fully-distributed algorithm for Nash equilibrium seeking in aggregative games over networks. The proposed scheme endows each agent with a gradient-based scheme equipped with a tracking mechanism to locally reconstruct the aggregative variable, which is not available to the agents. We show that our method falls into the framework of singularly perturbed systems, as it involves the interconnection between a fast subsystem - the global information reconstruction dynamics - with a slow one concerning the optimization of the local strategies. This perspective plays a key role in analyzing the scheme with a constant stepsize, and in proving its linear convergence to the Nash equilibrium in strongly monotone games with local constraints. By exploiting the flexibility of our aggregative variable definition (not necessarily the arithmetic average of the agents' strategy), we show the efficacy of our algorithm on a realistic voltage support case study for the smart grid.

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arXiv2025

Identification of non-causal systems with random switching modes (Extended Version)

We consider the identification of non-causal systems with random switching modes (NCSRSM), a class of models essential for describing typical power load management and department store inventory dynamics. The simultaneous identification of causal-andanticausal subsystems, along with the presence of random switching sequences, however, make the overall identification problem particularly challenging. To this end, we develop an expectation-maximization (EM) based system identification technique, where the E-step proposes a modified Kalman filter (KF) to estimate the states and switching sequences of causal-and-anticausal subsystems, while the M-step consists in a switching least-squares algorithm to estimate the parameters of individual subsystems. We establish the main convergence features of the proposed identification procedure, also providing bounds on the parameter estimation errors under mild conditions. Finally, the effectiveness of our identification method is validated through two numerical simulations.

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arXiv2025

Actively learning equilibria in Nash games with misleading information

We develop a scheme based on active learning to compute equilibria in a generalized Nash equilibrium problem (GNEP). Specifically, an external observer (or entity), with little knowledge on the multi-agent process at hand, collects sensible data by probing the agents' best-response (BR) mappings, which are then used to recursively update local parametric estimates of these mappings. Unlike [1], we consider the realistic case in which the agents share corrupted information with the external entity for, e.g., protecting their privacy. Inspired by a popular approach in stochastic optimization, we endow the external observer with an inexact proximal scheme for updating the local BR proxies. This technique will prove key to establishing the convergence of our scheme under standard assumptions, thereby enabling the external observer to predict an equilibrium strategy even when relying on masked information.

math.OC↗

arXiv2025

Fault-tolerant control of nonlinear systems: An inductive synthesis approach

Actuator faults heavily affect the performance and stability of control systems, an issue that is even more critical for systems required to operate autonomously under adverse environmental conditions, such as unmanned vehicles. To this end, passive fault-tolerant control (PFTC) systems can be employed, namely fixed-gain control laws that guarantee stability both in the nominal case and in the event of faults. In this paper, we propose a counterexample guided inductive synthesis (CEGIS)-based approach to design reliable PFTC policies for nonlinear control systems affected by partial, or total, actuator faults. Our approach enjoys finite-time convergence guarantees and extends available techniques by considering nonlinear dynamics with possible fault conditions. Extensive numerical simulations illustrate how the proposed method can be applied to realistic operational scenarios involving the velocity and heading control of autonomous underwater vehicles (AUVs). Our PFTC technique exhibits comparatively low synthesis time (i.e. minutes) and minimal computational requirements, which render it is suitable for embedded applications with limited availability of energy and onboard power resources.

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arXiv2025

Neural network-based identification of state-space switching nonlinear systems

We design specific neural networks (NNs) for the identification of switching nonlinear systems in the state-space form, which explicitly model the switching behavior and address the inherent coupling between system parameters and switching modes. This coupling is specifically addressed by leveraging the expectation-maximization (EM) framework. In particular, our technique will combine a moving window approach in the E-step to efficiently estimate the switching sequence, together with an extended Kalman filter (EKF) in the M-step to train the NNs with a quadratic convergence rate. Extensive numerical simulations, involving both academic examples and a battery charge management system case study, illustrate that our technique outperforms available ones in terms of parameter estimation accuracy, model fitting, and switching sequence identification.

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arXiv2024

Identification of non-causal systems with arbitrary switching modes

We consider the identification of non-causal systems with arbitrary switching modes (NCS-ASM), a class of models essential for describing typical power load management and department store inventory dynamics. The simultaneous identification of causal-and-anticausal subsystems, along with the presence of possibly random switching sequences, however, make the overall identification problem particularly challenging. To this end, we develop an expectation-maximization (EM) based system identification technique, where the E-step proposes a modified Kalman filter (KF) to estimate the states and switching sequences of causal-and-anticausal subsystems, while the M-step consists in a switching least-squares algorithm to estimate the parameters of individual subsystems. We establish the main convergence features of the proposed identification procedure, also providing bounds on the parameter estimation errors under mild conditions. Finally, the effectiveness of our identification method is validated through two numerical simulations.

cs.IT↗

arXiv2024

A Gauss-Seidel method for solving multi-leader-multi-follower games

We design a computational approach to find equilibria in a class of Nash games possessing a hierarchical structure. By using tools from mixed-integer optimization and the characterization of variational equilibria in terms of the Karush-Kuhn-Tucker conditions, we propose a mixed-integer game formulation for solving this challenging class of problems. Besides providing an equivalent reformulation, we design a proximal Gauss--Seidel method with global convergence guarantees in case the game enjoys a potential structure. We finally corroborate the numerical performance of the algorithm on a novel instance of the ride-hail market problem.

math.OC↗

arXiv2024

A neural network-based approach to hybrid systems identification for control

We consider the problem of designing a machine learning-based model of an unknown dynamical system from a finite number of (state-input)-successor state data points, such that the model obtained is also suitable for optimal control design. We adopt a neural network (NN) architecture that, once suitably trained, yields a hybrid system with continuous piecewise-affine (PWA) dynamics that is differentiable with respect to the network's parameters, thereby enabling the use of derivative-based training procedures. We show that a careful choice of our NN's weights produces a hybrid system model with structural properties that are highly favorable when used as part of a finite horizon optimal control problem (OCP). Specifically, we rely on available results to establish that optimal solutions with strong local optimality guarantees can be computed via nonlinear programming (NLP), in contrast to classical OCPs for general hybrid systems which typically require mixed-integer optimization. Besides being well-suited for optimal control design, numerical simulations illustrate that our NN-based technique enjoys very similar performance to state-of-the-art system identification methods for hybrid systems and it is competitive on nonlinear benchmarks.

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arXiv2023

Probably approximately correct stability of allocations in uncertain coalitional games with private sampling

We study coalitional games with exogenous uncertainty in the coalition value, in which each agent is allowed to have private samples of the uncertainty. As a consequence, the agents may have a different perception of stability of the grand coalition. In this context, we propose a novel methodology to study the out-of-sample coalitional rationality of allocations in the set of stable allocations (i.e., the core). Our analysis builds on the framework of probably approximately correct learning. Initially, we state a priori and a posteriori guarantees for the entire core. Furthermore, we provide a distributed algorithm to compute a compression set that determines the generalization properties of the a posteriori statements. We then refine our probabilistic robustness bounds by specialising the analysis to a single payoff allocation, taking, also in this case, both a priori and a posteriori approaches. Finally, we consider a relaxed $\zeta$-core to include nearby allocations and also address the case of empty core. For this case, probabilistic statements are given on the eventual stability of allocations in the $\zeta$-core.

math.OC↗

arXiv2023

Best-response algorithms for a class of monotone Nash equilibrium problems with mixed-integer variables

We characterize the convergence properties of traditional best-response (BR) algorithms in computing solutions to mixed-integer Nash equilibrium problems (MI-NEPs) that turn into a class of monotone Nash equilibrium problems (NEPs) once relaxed the integer restrictions. We show that the sequence produced by a Jacobi/Gauss-Seidel BR method always approaches a bounded region containing the entire solution set of the MI-NEP, whose tightness depends on the problem data, and it is related to the degree of strong monotonicity of the relaxed NEP. When the underlying algorithm is applied to the relaxed NEP, we establish data-dependent complexity results characterizing its convergence to the unique solution of the NEP. In addition, we derive one of the very few sufficient conditions for the existence of solutions to MI-NEPs. The theoretical results developed bring important practical benefits, illustrated on a numerical instance of a smart building control application.

math.OC↗

arXiv2023

Generalized uncertain Nash games: Reformulation and robust equilibrium seeking -- Extended version

We consider generalized Nash equilibrium problems (GNEPs) with linear coupling constraints affected by both local (i.e., agent-wise) and global (i.e., shared resources) disturbances taking values in polyhedral uncertainty sets. By making use of traditional tools borrowed from robust optimization, for this class of problems we derive a tractable, finite-dimensional reformulation leading to a deterministic ''extended game'', and we show that this latter still amounts to a GNEP featuring generalized Nash equilibria ''in the worst-case''. We then design a fully-distributed, accelerated algorithm based on monotone operator theory, which enjoys convergence towards a Nash equilibrium of the original, uncertain game under weak structural assumptions. Finally, we illustrate the effectiveness of the proposed distributed scheme through numerical simulations

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arXiv2023

Counter-example guided inductive synthesis of control Lyapunov functions for uncertain systems

We propose a counter-example guided inductive synthesis (CEGIS) scheme for the design of control Lyapunov functions and associated state-feedback controllers for linear systems affected by parametric uncertainty with arbitrary shape. In the CEGIS framework, a learner iteratively proposes a candidate control Lyapunov function and a tailored controller by solving a linear matrix inequality (LMI) feasibility problem, while a verifier either falsifies the current candidate by producing a counter-example to be considered at the next iteration, or it certifies that the tentative control Lyapunov function actually enjoys such feature. We investigate the Lipschitz continuity of the objective function of the global optimization problem solved by the verifier, which is key to establish the convergence of our method in a finite number of iterations. Numerical simulations confirm the effectiveness of the proposed approach.

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arXiv2023

Incentives and co-evolution: Steering linear dynamical systems with noncooperative agents

Modern socio-technical systems typically consist of many interconnected users and competing service providers, where notions like market equilibrium are tightly connected to the ``evolution'' of the network of users. In this paper, we model the users' dynamics as a linear dynamical system, and the service providers as agents taking part to a generalized Nash game, whose outcome coincides with the input of the users' dynamics. We thus characterize the notion of co-evolution of the market and the network dynamics and derive dissipativity-based conditions leading to a pertinent notion of equilibrium. We then focus on the control design and adopt the light-touch policy to incentivize or penalize the service providers as little as possible, while steering the networked system to a desirable outcome. We also provide a dimensionality-reduction procedure, which offers network-size independent conditions. Finally, we illustrate our novel notions and algorithms on a simulation setup stemming from digital market regulations for influencers, a topic of growing interest.

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arXiv2022

An active learning method for solving competitive multi-agent decision-making and control problems

To identify a stationary action profile for a population of competitive agents, each executing private strategies, we introduce a novel active-learning scheme where a centralized external observer (or entity) can probe the agents' reactions and recursively update simple local parametric estimates of the action-reaction mappings. Under very general working assumptions (not even assuming that a stationary profile exists), sufficient conditions are established to assess the asymptotic properties of the proposed active learning methodology so that, if the parameters characterizing the action-reaction mappings converge, a stationary action profile is achieved. Such conditions hence act also as certificates for the existence of such a profile. Extensive numerical simulations involving typical competitive multi-agent control and decision-making problems illustrate the practical effectiveness of the proposed learning-based approach.

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arXiv2022

Tracking-based distributed equilibrium seeking for aggregative games

We propose fully-distributed algorithms for Nash equilibrium seeking in aggregative games over networks. We first consider the case where local constraints are present and we design an algorithm combining, for each agent, (i) the projected pseudo-gradient descent and (ii) a tracking mechanism to locally reconstruct the aggregative variable. To handle coupling constraints arising in generalized settings, we propose another distributed algorithm based on (i) a recently emerged augmented primal-dual scheme and (ii) two tracking mechanisms to reconstruct, for each agent, both the aggregative variable and the coupling constraint satisfaction. Leveraging tools from singular perturbations analysis, we prove linear convergence to the Nash equilibrium for both schemes. Finally, we run extensive numerical simulations to confirm the effectiveness of our methods and compare them with state-of-the-art distributed equilibrium-seeking algorithms.

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