从动力系统视角揭示推荐系统中流行度偏见的形成机制
Stay or Stray - A Dynamical Systems Viewpoint of Popularity Bias
- 用双时间尺度随机逼近建模用户与推荐系统的动态演化
- 理论证明在特定条件下流行度偏见必然产生，否则可保持用户公平
- 基于真实音乐平台数据验证，为公平推荐提供理论依据
推荐系统中的流行度偏见表现为多数用户群体产生大量交互数据，导致系统持续偏向该群体，损害小众用户推荐质量。尽管已有大量实证研究，但其动态形成机制尚不清晰。本文从动力系统角度分析推荐模型更新与用户参与的耦合演化过程，构建随机过程并基于双时间尺度随机逼近的常微分方程框架分析其渐近行为。我们刻画了该动力系统的平衡点，推导出流行度偏见必然涌现的条件，以及所有用户类别可对称留存的条件。通过合成数据和大型商业音乐推荐平台的真实生产日志实验，验证了理论结果。
原文摘要 · Abstract (English)
Popularity bias in recommendation systems arises when a majority user class generates disproportionate interaction data, causing the system to increasingly favour it while degrading recommendation quality for niche users. While extensive empirical evidence of popularity bias exists, the dynamics leading to its emergence are not well understood. In this work, we study the coupled evolution of recommender model updates and user engagement through the lens of dynamical systems. We formulate a stochastic process and analyse its asymptotic behaviour through an ordinary differential equation (ODE) framework grounded in two-time-scale stochastic approximation. We characterise the equilibrium points of this dynamical system, and derive conditions under which popularity bias is provably emergent, as well as conditions under which symmetric retention of all user classes is possible. We conduct experiments on synthetic data and real-world production logs derived from a large-scale commercial music recommendation platform to validate our theoretical results.
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