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Network-aware Recommender System via Online Feedback Optimization

Sanjay Chandrasekaran, Giulia De Pasquale, Giuseppe Belgioioso, Florian Dörfler

TL;DR

The approach extends online feedback optimization to develop a recommender system that trades off users engagement and polarization reduction, while relying solely on online click data to mitigate polarization.

Abstract

Personalized content on social platforms can exacerbate negative phenomena such as polarization, partly due to the feedback interactions between recommendations and the users. In this paper, we present a control-theoretic recommender system that explicitly accounts for this feedback loop to mitigate polarization. Our approach extends online feedback optimization - a control paradigm for steady-state optimization of dynamical systems - to develop a recommender system that trades off users engagement and polarization reduction, while relying solely on online click data. We establish theoretical guarantees for optimality and stability of the proposed design and validate its effectiveness via numerical experiments with a user population governed by Friedkin-Johnsen dynamics. Our results show these "network-aware" recommendations can significantly reduce polarization while maintaining high levels of user engagement.

Network-aware Recommender System via Online Feedback Optimization

TL;DR

The approach extends online feedback optimization to develop a recommender system that trades off users engagement and polarization reduction, while relying solely on online click data to mitigate polarization.

Abstract

Personalized content on social platforms can exacerbate negative phenomena such as polarization, partly due to the feedback interactions between recommendations and the users. In this paper, we present a control-theoretic recommender system that explicitly accounts for this feedback loop to mitigate polarization. Our approach extends online feedback optimization - a control paradigm for steady-state optimization of dynamical systems - to develop a recommender system that trades off users engagement and polarization reduction, while relying solely on online click data. We establish theoretical guarantees for optimality and stability of the proposed design and validate its effectiveness via numerical experiments with a user population governed by Friedkin-Johnsen dynamics. Our results show these "network-aware" recommendations can significantly reduce polarization while maintaining high levels of user engagement.
Paper Structure (27 sections, 8 theorems, 65 equations, 8 figures, 2 tables, 2 algorithms)

This paper contains 27 sections, 8 theorems, 65 equations, 8 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem setup
  3. Social Network Modelling
  4. Problem formulation
  5. Recommender system design
  6. Level I: Opinions & Clicking Behaviour Estimation
  7. Opinion Estimation
  8. Clicking Behaviour Estimation
  9. Level II: Online Sensitivity Learning
  10. Kalman Filter for Sensitivity Learning
  11. Level III: Gradient Estimation & Optimization
  12. Gradient Estimation
  13. Projected Gradient Descent Algorithm
  14. Closed-loop Convergence Guarantees
  15. Numerical Case Studies
  16. ...and 12 more sections

Key Result

Lemma 1

Given a globally $\beta$-smooth map $\Phi: \mathbb{R}^n \rightarrow \mathbb{R}$, then $\Phi(x_1) - \Phi(x_2) - \nabla \Phi^\top (x_2) (x_1-x_2) \leq \frac{1}{2}\beta\lVert x_1-x_2\rVert^2$. Further, if $\Phi$ is twice continuously-differentiable, then $\lVert\nabla^2 \Phi\rVert \leq \beta$.

Figures (8)

  • Figure 1: Closed-loop interconnection between users' opinion in a social network and the proposed recommender system.
  • Figure 2: Block diagram of the proposed recommender system design with the three levels. Level I: Opinion and clicking behaviour estimation, Level II: Sensitivity estimation, Level III: Optimization.
  • Figure 3: Evolution of the fixed-point residuals $\lVert\mathcal{G}(p^k)\rVert^2$ for the algorithms in Table \ref{['methodscomparisontable']}. The bold lines represent the mean and the shaded region are the $\pm 1$ standard deviation across the $50$ Monte-Carlo trials.
  • Figure 4: Evolution of the sensitivity estimation error in methods $M_2-M_4$. The bold lines represent the mean and the shaded region are the $\pm 1$ standard deviation across the $50$ Monte-Carlo trials.
  • Figure 5: Illustration of opinion estimation in method $M_4$.
  • ...and 3 more figures

Theorems & Definitions (24)

  • Definition 1: Minimal modulus of continuityBRENEIS
  • Definition 2: Persistently exciting input WILLEMS
  • Definition 3: Global $\beta$-smoothness nesterov
  • Lemma 1: Properties of $\beta$-smooth functions nesterov
  • Example 1: Extended Friedkin--Johnsen model
  • Example 2: Extremity confirmation bias rossi
  • Remark 1
  • Lemma 2: Opinion estimation error
  • proof
  • Lemma 3: Clicking behaviour estimation error
  • ...and 14 more