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Control Strategies for Recommendation Systems in Social Networks

Ben Sprenger, Giulia De Pasquale, Raffaele Soloperto, John Lygeros, Florian Dörfler

TL;DR

This work integrates recommendation-system inputs into opinion dynamics by extending the Friedkin-Johnsen model to a closed-loop setting and studying control strategies to maximize engagement. It develops a model-free controller and a model-based MPC benchmark, both aimed at steering user opinions within a bounded domain while maximizing engagement under an $\ell_2$-type cost $\theta(x,u)$. Theoretical analysis establishes stability for $\lambda$-connected networks, derives steady-state bounds, and compares MF and MB performance, with MB sometimes outperforming MF at the cost of larger opinion shifts in certain scenarios. Numerical experiments on networks with varying connectivity demonstrate the practical efficacy and social-risk tradeoffs of the proposed approaches, pointing to future work on mitigation of radicalization and improved observability for opinion inference.

Abstract

A closed-loop control model to analyze the impact of recommendation systems on opinion dynamics within social networks is introduced. The core contribution is the development and formalization of model-free and model-based approaches to recommendation system design, integrating the dynamics of social interactions within networks via an extension of the Friedkin-Johnsen (FJ) model. Comparative analysis and numerical simulations demonstrate the effectiveness of the proposed control strategies in maximizing user engagement and their potential for influencing opinion formation processes.

Control Strategies for Recommendation Systems in Social Networks

TL;DR

This work integrates recommendation-system inputs into opinion dynamics by extending the Friedkin-Johnsen model to a closed-loop setting and studying control strategies to maximize engagement. It develops a model-free controller and a model-based MPC benchmark, both aimed at steering user opinions within a bounded domain while maximizing engagement under an -type cost . Theoretical analysis establishes stability for -connected networks, derives steady-state bounds, and compares MF and MB performance, with MB sometimes outperforming MF at the cost of larger opinion shifts in certain scenarios. Numerical experiments on networks with varying connectivity demonstrate the practical efficacy and social-risk tradeoffs of the proposed approaches, pointing to future work on mitigation of radicalization and improved observability for opinion inference.

Abstract

A closed-loop control model to analyze the impact of recommendation systems on opinion dynamics within social networks is introduced. The core contribution is the development and formalization of model-free and model-based approaches to recommendation system design, integrating the dynamics of social interactions within networks via an extension of the Friedkin-Johnsen (FJ) model. Comparative analysis and numerical simulations demonstrate the effectiveness of the proposed control strategies in maximizing user engagement and their potential for influencing opinion formation processes.
Paper Structure (14 sections, 8 theorems, 21 equations, 5 figures)

This paper contains 14 sections, 8 theorems, 21 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Opinion dynamics: Friedkin-Johnsen model
  4. The recommendation system
  5. Opinion manipulation
  6. Desired objective
  7. Proposed Approaches
  8. Model-free approach
  9. Model-based approach
  10. Comparison between MF and MB approaches
  11. Numerical Simulations
  12. Approaches comparison
  13. Fully prejudiced user
  14. Conclusions

Key Result

Theorem II.1

Given the FJ model FJ, the state $o^*$, defined as is the only equilibrium point of FJ and is asymptotically stable if and only if the system is $\lambda$-connected.

Figures (5)

  • Figure 1: Recommendation system and social network feedback loop.
  • Figure 2: MPC cost improvement over Model-Free.
  • Figure 3: Opinion shift with MPC and Model-Free.
  • Figure 4: User network with radical user and recommendation system.
  • Figure 5: Opinion evolution for the network with a radical user.

Theorems & Definitions (18)

  • Definition II.1: Prejudice and P-dependence
  • Definition II.2: $\lambda$-Connectivity
  • Theorem II.1: Convergence guarantees AVP-RT:17
  • Proposition II.2: Well-posedness
  • proof
  • Proposition II.3: Reachability bounds
  • proof
  • Theorem III.1: MF and FJ analogy
  • proof
  • Lemma III.2: MB Steady state
  • ...and 8 more