# Online Minimization of Polarization and Disagreement via Low-Rank Matrix Bandits

arXiv: https://arxiv.org/abs/2510.00803 · HTML: https://mlsanity.com/paper/2510.00803/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Builds on (most cited first, 17 of 17)

- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Bilinear Bandits with Low-rank Structure](https://mlsanity.com/paper/1901.02470/) (2019)
- [Low-Rank Generalized Linear Bandit Problems](https://mlsanity.com/paper/2006.02948/) (2020)
- [Stochastic Rank-1 Bandits](https://mlsanity.com/paper/1608.03023/) (2016)
- [Efficient Frameworks for Generalized Low-Rank Matrix Bandit Problems](https://mlsanity.com/paper/2401.07298/) (2024)
- [Minimizing Polarization and Disagreement in Social Networks](https://mlsanity.com/paper/1712.09948/) (2017)
- [Optimal Gradient-based Algorithms for Non-concave Bandit Optimization](https://mlsanity.com/paper/2107.04518/) (2021)
- [Efficient Low-Rank Matrix Estimation, Experimental Design, and Arm-Set-Dependent Low-Rank Bandits](https://mlsanity.com/paper/2402.11156/) (2024)
- [Low-rank Matrix Bandits with Heavy-tailed Rewards](https://mlsanity.com/paper/2404.17709/) (2024)
- [On the Relationship Between Relevance and Conflict in Online Social Link Recommendations](https://mlsanity.com/paper/2310.14076/) (2023)
- [GL-LowPopArt: A Nearly Instance-Wise Minimax-Optimal Estimator for Generalized Low-Rank Trace Regression](https://mlsanity.com/paper/2506.03074/) (2025)
- [Generalized Low-Rank Matrix Contextual Bandits with Graph Information](https://mlsanity.com/paper/2507.17528/) (2025)
- [Optimizing Social Network Interventions via Hypergradient-Based Recommender System Design](https://mlsanity.com/paper/2502.12973/) (2025)
- [Minimizing Polarization in Noisy Leader-Follower Opinion Dynamics](https://mlsanity.com/paper/2308.07008/) (2023)
- [Rebalancing Social Feed to Minimize Polarization and Disagreement](https://mlsanity.com/paper/2308.14486/) (2023)
- [Sublinear-Time Opinion Estimation in the Friedkin--Johnsen Model](https://mlsanity.com/paper/2404.16464/) (2024)
- [Minimizing Polarization and Disagreement in the Friedkin-Johnsen Model with Unknown Innate Opinions](https://mlsanity.com/paper/2501.16076/) (2025)

## Built on by (most cited first, 1 of 1)

- [PACIFIER: Pacing Opinion Depolarization via a Unified Graph Learning Framework](https://mlsanity.com/paper/2602.23390/) (2026)

## Abstract (arXiv)

We study the problem of minimizing polarization and disagreement in the Friedkin-Johnsen opinion dynamics model under incomplete information. Unlike prior work that assumes a static setting with full knowledge of agents' innate opinions, we address the more realistic online setting where innate opinions are unknown and must be learned through sequential observations. This novel setting, which naturally mirrors periodic interventions on social media platforms, is formulated as a regret minimization problem, establishing a key connection between algorithmic interventions on social media platforms and the theory of multi-armed bandits. In our formulation, a learner observes only a scalar feedback of the overall polarization and disagreement after an intervention. For this novel bandit problem, we propose a two-stage algorithm based on low-rank matrix bandits. The algorithm first performs subspace estimation to identify an underlying low-dimensional structure, and then employs a linear bandit algorithm within the compact dimensional representation derived from the estimated subspace. We show that our algorithm achieves the cumulative regret of widetildeObig(max(tfrac1kappa,√|V|)√|V|Tbig) over time horizon T, where V is the set of agents and kappa is a parameter dependent on the diversity of interventions. Empirical results validate that our algorithm significantly outperforms a linear bandit baseline in terms of both cumulative regret and running time.