arXiv subjects

Paolo Frasca

Publications and source records attributed to Paolo Frasca.

At least 19 recordsLinked to original sources

arXiv2026

Bayesian Equilibria of Heterogeneous Non-Atomic Routing Games with Private Information

We study non-atomic Bayesian routing games whereby a transportation network is shared by two types of traffic: a coordinated fleet and a mass of selfish users. The links in the network are characterized by travel time functions that depend both on the aggregate flow on the link and on a random state of the world $W$ that, in general, is not directly observable. Rather, we assume that both the fleet coordinator and the selfish users know the prior distribution of $W$, observe (different) private messages that are correlated with $W$ and possibly among themselves, and make routing decisions based on such heterogeneous partial information. Under the assumption that both the state of the world and the private message sets are finite, we prove the existence and uniqueness of a Bayesian equilibrium for the ensuing Bayesian routing game.

math.OC↗

arXiv2026

Recommender Systems as Control Systems

We propose a control-theoretic interpretation of recommender systems and use this perspective to analyze how fairness interventions shape long-term system behavior. Fairness concerns arise for both users and creators, ranging from opinion polarization and representation bias on the user side to popularity bias on the creator side. A central insight of our analysis is that fairness should not be viewed as a simple trade-off against utility. When optimized over time, it can in fact be beneficial for overall system performance. Realizing these gains, however, requires a clear understanding of the underlying dynamics.

eess.SY↗

arXiv2026

Optimal Control Synthesis of Closed-Loop Recommendation Systems over Social Networks

This paper addresses the problem of designing recommendation systems for social networks and e-commerce platforms from a control-theoretic perspective. We treat the design of recommendation systems as a state-feedback infinite-horizon optimal control problem with a performance index that (i) rewards alignment and engagement, (ii) penalizes polarization and large deviations from an uncontrolled baseline, and (iii) regularizes exposure across neighboring users. The recommendation entries are fed to the platform users, who are assumed to follow a networked, multi-topic, continuous-time opinion dynamics. We show that the designed control yields a stabilizing recommendation system under simple algebraic spectral conditions on the weights that encode the platform's preference for engagement, stability of preferences, polarization, and cross-user diversity. Conversely, we show that when ill-posed weights are selected in the optimal control problem (namely, when engagement is excessively rewarded), the closed-loop system can exhibit destabilizing, pathological behaviors that conflict with the design objectives.

eess.SY↗

arXiv2025

On the Perturbed Projection-Based Distributed Gradient-Descent Algorithm: A Fully-Distributed Adaptive Redesign

In this work, we revisit a classical distributed gradient-descent algorithm, introducing an interesting class of perturbed multi-agent systems. The state of each subsystem represents a local estimate of a solution to the global optimization problem. Thereby, the network is required to minimize local cost functions, while gathering the local estimates around a common value. Such a complex task suggests the interplay of consensus-based dynamics with gradient-descent dynamics. The latter descent dynamics involves the projection operator, which is assumed to provide corrupted projections of a specific form, reminiscent of existing (fast) projection algorithms. Hence, for the resulting class of perturbed networks, we are able to adaptively tune some gains in a fully distributed fashion, to approach the optimal consensus set up to arbitrary-desired precision.

math.OC↗

arXiv2025

Opinion Dynamics on Signed Graphs and Graphons

In this paper, we make use of graphon theory to study opinion dynamics on large undirected networks. The opinion dynamics models that we take into consideration allow for negative interactions between the individuals, whose opinions can thus grow apart. We consider both the repelling and the opposing models of negative interactions, which have been studied in the literature. We define the repelling and the opposing dynamics on signed graphons and we show that their initial value problem solutions exist and are unique. We then show that, in a suitable sense, the graphon dynamics is a good approximation of the dynamics on large graphs that converge to a graphon. This result applies to large random graphs that are sampled according to a graphon (W-random graphs), for which we provide a new convergence result under very general assumptions.

cs.SI↗

arXiv2025

A Coupled Friedkin-Johnsen Model of Popularity Dynamics in Social Media

Popularity dynamics in social media depend on a complex interplay of social influence between users and popularity-based recommendations that are provided by the platforms. In this work, we introduce a discrete-time dynamical system to model the evolution of popularity on social media. Our model generalizes the well-known Friedkin-Johnsen model to a set of influencers vying for popularity. We study the asymptotic behavior of this model and illustrate it with numerical examples. Our results highlight the interplay of social influence, past popularity, and content quality in determining the popularity of influencers.

cs.SI↗

arXiv2025

Optimal Policy Design for Repeated Decision-Making under Social Influence

In this paper, we present a novel model to characterize individual tendencies in repeated decision-making scenarios, with the goal of designing model-based control strategies that promote virtuous choices amidst social and external influences. Our approach builds on the classical Friedkin and Johnsen model of social influence, extending it to include random factors (e.g., inherent variability in individual needs) and controllable external inputs. We explicitly account for the temporal separation between two processes that shape opinion dynamics: individual decision-making and social imitation. While individual decisions occur at regular, frequent intervals, the influence of social imitation unfolds over longer periods. The inclusion of random factors naturally leads to dynamics that do not converge in the classical sense. However, under specific conditions, we prove that opinions exhibit ergodic behavior. Building on this result, we propose a constrained asymptotic optimal control problem designed to foster, on average, social acceptance of a target action within a network. To address the transient dynamics of opinions, we reformulate this problem within a Model Predictive Control (MPC) framework. Simulations highlight the significance of accounting for these transient effects in steering individuals toward virtuous choices while managing policy costs.

eess.SY↗

arXiv2024

Selfish routing on transportation networks with supply and demand constraints

Traditional non-atomic selfish routing games present some limitations in properly modeling road traffic. This paper introduces a novel type of non-atomic selfish routing game leveraging concepts from Daganzo's cell transmission model (CTM). Each network link is characterized by a supply and demand mechanism that enforces capacity constraints based on current density, providing a more accurate representation of real-world traffic phenomena. We characterize the Wardrop equilibria and social optima of this game and identify a previously unrecognized inefficiency in selfish routing: partially transferring Wardrop equilibria, where only part of the exogenous flow traverses the network.

math.OC↗

arXiv2024

Individual based SIS models on (not so) dense large random networks

Starting from a stochastic individual-based description of an SIS epidemic spreading on a random network, we study the dynamics when the size $n$ of the network tends to infinity. We recover in the limit an infinite-dimensional integro-differential equation studied by Delmas, Dronnier and Zitt (2022) for an SIS epidemic propagating on a graphon. Our work covers the case of dense and sparse graphs, provided that the number of edges grows faster than $n$, but not the case of very sparse graphs with $O(n)$ edges. In order to establish our limit theorem, we have to deal with both the convergence of the random graphs to the graphon and the convergence of the stochastic process spreading on top of these random structures: in particular, we propose a coupling between the process of interest and an epidemic that spreads on the complete graph but with a modified infection rate. Keywords: Random graph, mathematical models of epidemics, measure-valued process, large network limit, limit theorem, graphon.

math.PR↗

arXiv2024

Opinion dynamics on signed graphs and graphons: Beyond the piece-wise constant case (Extended version)

In this paper we make use of graphon theory to study opinion dynamics on large undirected networks. The opinion dynamics models that we take into consideration allow for negative interactions between the individuals, i.e. competing entities whose opinions can grow apart. We consider both the repelling model and the opposing model that are studied in the literature. We define the repelling and the opposing dynamics on graphons and we show that their initial value problem's solutions exist and are unique. We then show that the graphon dynamics well approximate the dynamics on large graphs that converge to a graphon. This result applies to large random graphs that are sampled according to a graphon. All these facts are illustrated in an extended numerical example.

physics.soc-ph↗

arXiv2024

On the impact of coordinated fleets size on traffic efficiency

We investigate a traffic assignment problem on a transportation network, considering both the demands of individual drivers and of a large fleet controlled by a central operator (minimizing the fleet's average travel time). We formulate this problem as a two-player convex game and we study how the size of the coordinated fleet, measured in terms of share of the total demand, influences the Price of Anarchy (PoA). We show that, for two-terminal networks, there are cases in which the fleet must reach a minimum share before actually affecting the PoA, which otherwise remains unchanged. Moreover, for parallel networks we prove that, under suitable assumptions, the PoA is monotonically non-increasing in the fleet share.

cs.GT↗

arXiv2024

Corrections to and improvements on results from "The Laplacian spectrum of large graphs sampled from graphons"

In this note we correct the proof of Proposition 4 in our paper "The Laplacian Spectrum of Large Graphs Sampled from Graphons" (arXiv:2004.09177) and we improve several results therein. To this end, we prove a new concentration lemma about degrees and Laplacian eigenvalues. This lemma allows us to improve several bounds and to dispense from assuming that the graphon is bounded away from zero in several results. This extension leads, in particular, to correct the proof of Proposition 4. Additionally, we extend Proposition 4 to graphs that are sampled from graphons by using deterministic latent variables.

math.OC↗

arXiv2024

Optimal policy design for decision problems under social influence

This paper focuses on describing the impact of policy actions on individuals' opinions in the presence of social and external influences toward proposing preliminary nudging strategies to achieve a cost-effectiveness trade-off. To this end, we extend the classical Friedkin and Johnsen model of opinion dynamics to incorporate random factors, such as variability in individual predispositions due to uncontrolled events (e.g., modeling the impact of the weather on daily mobility choices), and describe the impact of personalized policies. Furthermore, we formulate an optimal control problem aimed at fostering the social acceptance of particular actions/choices within the network. Through our analysis and numerical simulations, we illustrate the features of the proposed model in the absence of nudging and the effectiveness of the proposed (optimal) nudging strategies.

eess.SY↗

arXiv2024

SIS epidemics on open networks: A replacement-based approximation

In this paper we analyze continuous-time SIS epidemics subject to arrivals and departures of agents, by using an approximated process based on replacements. In defining the SIS dynamics in an open network, we consider a stochastic setting in which arrivals and departures take place according to Poisson processes with similar rates, and the new value of the infection probability of an arriving agent is drawn from a continuous distribution. Since the system size changes with time, we define an approximated process, in which replacements take place instead of arrivals and departures, and we focus on the evolution of an aggregate measure of the level of infection. So long as the reproduction number is less than one, the long-term behavior of this function measures the impact of the changes of the set of agents in the epidemic. We derive upper bounds for the expectation and variance of this function and we include a numerical example to show that the approximated process is close to the original SIS process.

eess.SY↗

arXiv2023

Random Coordinate Descent for Resource Allocation in Open Multi-Agent Systems

We propose a method for analyzing the distributed random coordinate descent algorithm for solving separable resource allocation problems in the context of an open multiagent system, where agents can be replaced during the process. In particular, we characterize the evolution of the distance to the minimizer in expectation by following a time-varying optimization approach which builds on two components. First, we establish the linear convergence of the algorithm in closed systems, in terms of the estimate towards the minimizer, for general graphs and appropriate step-size. Second, we estimate the change of the optimal solution after a replacement, in order to evaluate its effect on the distance between the current estimate and the minimizer. From these two elements, we derive stability conditions in open systems and establish the linear convergence of the algorithm towards a steady-state expected error. Our results enable to characterize the trade-off between speed of convergence and robustness to agent replacements, under the assumptions that local functions are smooth, strongly convex, and have their minimizers located in a given ball. The approach proposed in this paper can moreover be extended to other algorithms guaranteeing linear convergence in closed system.

cs.MA↗

arXiv2023

Resilience in Platoons of Cooperative Heterogeneous Vehicles: Self-organization Strategies and Provably-correct Design

This work proposes provably-correct self-organizing strategies for platoons of heterogeneous vehicles. We refer to self-organization as the capability of a platoon to autonomously homogenize to a common group behavior. We show that self-organization promotes resilience to acceleration limits and communication failures, i.e., homogenizing to a common group behavior makes the platoon recover from these causes of impairments. In the presence of acceleration limits, resilience is achieved by self-organizing to a common constrained group behavior that prevents the vehicles from hitting their acceleration limits. In the presence of communication failures, resilience is achieved by self-organizing to a common group observer to estimate the missing information. Stability of the self-organization mechanism is studied analytically, and correctness with respect to traffic actions (e.g. emergency braking, cut-in, merging) is realized through a provably-correct safety layer. Numerical validations via the platooning toolbox OpenCDA in CARLA and via the CommonRoad platform confirm improved performance through self-organization and the provably-correct safety layer.

eess.SY↗

arXiv2023

Potential detrimental effects of real-time route recommendations in traffic networks

Navigation apps have become pervasive in providing real-time route recommendations to travelers willing to minimize their travel times. However, such technologies introduce new complexities, raising concerns about their overall impact on traffic networks. This paper focuses on evaluating the effect of navigation apps on traffic flows, particularly examining how real-time route recommendations influence network efficiency and congestion. Using a dynamical network flow model, we study traffic dynamics between an origin-destination pair, where a fraction of drivers follow app recommendations while others rely on fixed route preferences. By incorporating supply-demand mechanisms to account for capacity and volume constraints on routes, we uncover partial demand transfer, i.e., only a portion of the traffic demand is able to traverse the network, while the rest builds up congestion at the origin. We prove that the dynamics converges to a globally stable equilibrium and we provide a detailed analysis of this equilibrium when the choices of the informed drivers follow a logit model, correlating the emergence of partial demand transfer to the penetration rate of navigation apps among users.

eess.SY↗

arXiv2023

On Lyapunov functions for open Hegselmann-Krause dynamics

In this paper, we provide a formulation of an open Hegselmann-Krause (HK) dynamics where agents can join and leave the system during the interactions. We consider a stochastic framework where the time instants corresponding to arrivals and departures are determined by homogeneous Poisson processes. Then, we provide a survey of Lyapunov functions based on global and local disagreement, whose asymptotic behavior can be used to measure the impact of arrivals and departures. After proving analytical results on these Lyapunov functions in the open system, we illustrate them through numerical simulations in two scenarios characterized by a different number of expected agents.

eess.SY↗