Optimizing Social Network Interventions via Hypergradient-Based Recommender System Design

TL;DR

This work tackles the polarization and disagreement amplification in social networks by formulating a differentiable bilevel optimization where the upper level edits network weights and the lower level follows Friedkin-Johnsen opinion dynamics. A gradient-based method, BeeRS, backprops through the equilibrium to compute the hypergradient efficiently via a single linear solve, enabling scalable optimization on networks with millions of variables. The approach outperforms state-of-the-art nonlinear solvers (IPOPT) by up to three orders of magnitude in runtime while achieving superior objective values, and it yields meaningful reductions in both polarization and disagreement on real datasets (e.g., Reddit, DBLP). The framework is modular, GPU-friendly, and adaptable to various differentiable objectives, offering practical possibilities for responsible recommender-system design under convex feasibility constraints.

Abstract

Although social networks have expanded the range of ideas and information accessible to users, they are also criticized for amplifying the polarization of user opinions. Given the inherent complexity of these phenomena, existing approaches to counteract these effects typically rely on handcrafted algorithms and heuristics. We propose an elegant solution: we act on the network weights that model user interactions on social networks (e.g., frequency of communication), to optimize a performance metric (e.g., polarization reduction), while users' opinions follow the classical Friedkin-Johnsen model. Our formulation gives rise to a challenging large-scale optimization problem with non-convex constraints, for which we develop a gradient-based algorithm. Our scheme is simple, scalable, and versatile, as it can readily integrate different, potentially non-convex, objectives. We demonstrate its merit by: (i) rapidly solving complex social network intervention problems with 3 million variables based on the Reddit and DBLP datasets; (ii) significantly outperforming competing approaches in terms of both computation time and disagreement reduction.

Figures (6)

• Figure 1: The mean runtime and $\pm$ 1 standard deviation over 100 runs of 1 iteration of \ref{['alg:algorithm']} on both a GPU and a CPU.
• Figure 2: The mean runtime and $\pm$ 1 standard deviation over 10 runs of \ref{['alg:algorithm']} and IPOPT (until convergence) on a CPU.
• Figure 3: Behavior of \ref{['alg:algorithm']} and \ref{['alg:nad']} (without regularization) in a toy example network. We plot disagreement as a function of weights $w$ for internal opinions $s_0 = 1$ and $s_1 = 0$. The feasible region is shown in white.
• Figure 4: Optimal edge weight modification in relation to external opinions connected by edge computed by three approaches. The horizontal and vertical axes show the external opinion before intervention at the tail and head of an edge, respectively. The color encodes the change of edge weight during the intervention, i.e., $w_{ij} - w_{ij}^{(0)}$.
• Figure 5: We vary the step size $\alpha$ and display the resulting number of iterations (left) and the achieved minimum cost (right) for some momentum parameters $\gamma$.

Theorems & Definitions (5)

• Proposition 2.1
• Proposition 3.1
• proof
• Lemma 6.1
• proof