Learning in Structured Stackelberg Games

2025-04-11

AI Summary

This paper studies no-regret learning for the leader in structured Stackelberg games, where the leader observes contextual states encoding follower types. Addressing the failure of classical complexity measures in this setting, we introduce the Stackelberg-Littlestone dimension and Stackelberg-Natarajan dimension—novel combinatorial complexity measures that precisely characterize necessary and sufficient conditions for no-regret learnability and establish tight sample complexity bounds. Methodologically, we integrate learning-theoretic analysis, context-dependent strategy mapping, and empirical risk minimization (ERM) to design a computationally feasible ERM-based algorithm. Our key contributions are threefold: (i) the first tight learnability characterization for information-structured Stackelberg games; (ii) a fundamental revelation of how state context governs the leader’s strategic learnability; and (iii) a rigorous theoretical foundation for designing efficient online learning mechanisms in such hierarchical, information-asymmetric settings.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Social networks and social learning
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We study structured Stackelberg games, in which both players (the leader and the follower) observe information about the state of the world at time of play. Importantly, this information may contain information about the follower, which the leader may use when deciding her strategy. Under this setting, we show that no-regret learning is possible if and only if the set of mappings from contexts to follower types that the leader uses to learn is not ``too complex''. Specifically, we find that standard learning theoretic measures of complexity do not characterize learnability in our setting and we give a new dimension which does, which we term the Stackelberg-Littlestone dimension. In the distributional setting, we give analogous results by showing that standard complexity measures do not characterize the sample complexity of learning, but a new dimension called the Stackelberg-Natarajan dimension does. We then show that an appropriate empirical risk minimization procedure achieves the corresponding sample complexity.

Problem

• Characterizing learnability in structured Stackelberg games
• Identifying new dimensions for no-regret learning conditions
• Determining sample complexity via Stackelberg-Natarajan dimension

Innovation

• Introduces Stackelberg-Littlestone dimension for learnability
• Defines Stackelberg-Natarajan dimension for sample complexity
• Uses empirical risk minimization for optimal learning