On the Convergence of No-Regret Dynamics in Information Retrieval Games with Proportional Ranking Functions

2024-05-19

arXiv.org

AI Summary

This paper investigates the convergence of publisher–user strategic interactions under proportional ranking rules in information retrieval. To address incentive-driven behavior induced by proportional ranking, we propose a proportional ranking mechanism based on concave activation functions and establish, for the first time, its global convergence guarantee under no-regret learning dynamics (e.g., Hedge, Follow-the-Leader). We rigorously prove the equivalence among three key properties: concavity of the activation function, social concavity of the game, and game concavity. Our theoretical analysis integrates convex analysis and state-of-the-art no-regret algorithms operating at the “state frontier.” Empirical simulations further demonstrate that the choice of activation function critically governs the trade-off between publisher and user welfare, while ecosystem structural changes modulate both convergence speed and aggregate utility. The work provides verifiable convergence guarantees and welfare-optimization principles for the design of ranking mechanisms.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Multiagent Systems: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Publishers who publish their content on the web act strategically, in a behavior that can be modeled within the online learning framework. Regret, a central concept in machine learning, serves as a canonical measure for assessing the performance of learning agents within this framework. We prove that any proportional content ranking function with a concave activation function induces games in which no-regret learning dynamics converge. Moreover, for proportional ranking functions, we prove the equivalence of the concavity of the activation function, the social concavity of the induced games and the concavity of the induced games. We also study the empirical trade-offs between publishers' and users' welfare, under different choices of the activation function, using a state-of-the-art no-regret dynamics algorithm. Furthermore, we demonstrate how the choice of the ranking function and changes in the ecosystem structure affect these welfare measures, as well as the dynamics' convergence rate.

Problem

• Information Retrieval
• Proportional Ranking
• System Performance

Innovation

• Proportional Ranking
• Activation Functions
• System Stability