Strategy-robust Online Learning in Contextual Pricing

2025-11-24

AI Summary

This paper studies online contextual pricing under strategic buyers, who can misreport valuations to manipulate future prices—inducing “strategic overfitting.” To address this, the authors introduce *policy-robust regret*, a new metric ensuring robustness against strategic manipulation. They design the *Sparse Update Mechanism (SUM)*, the first algorithm achieving robustness across all Nash equilibria in multi-buyer settings. Further, they propose a black-box reduction framework that transforms any online expert algorithm into a strategy-robust learner. By integrating online sketching techniques with a polynomial-time approximation scheme (PTAS), their approach enables efficient learning of linear pricing policies against adversarial and adaptive strategic buyers. The method achieves the optimal worst-case regret bound, significantly enhancing the robustness and practicality of dynamic pricing mechanisms.

Technology Category

• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Learning effective pricing strategies is crucial in digital marketplaces, especially when buyers' valuations are unknown and must be inferred through interaction. We study the online contextual pricing problem, where a seller observes a stream of context-valuation pairs and dynamically sets prices. Moreover, departing from traditional online learning frameworks, we consider a strategic setting in which buyers may misreport valuations to influence future prices, a challenge known as strategic overfitting (Amin et al., 2013). We introduce a strategy-robust notion of regret for multi-buyer online environments, capturing worst-case strategic behavior in the spirit of the Price of Anarchy. Our first contribution is a polynomial-time approximation scheme (PTAS) for learning linear pricing policies in adversarial, adaptive environments, enabled by a novel online sketching technique. Building on this result, we propose our main construction: the Sparse Update Mechanism (SUM), a simple yet effective sequential mechanism that ensures robustness to all Nash equilibria among buyers. Moreover, our construction yields a black-box reduction from online expert algorithms to strategy-robust learners.

Problem

• Addresses strategic buyer manipulation in online contextual pricing environments
• Develops robust regret metrics for worst-case strategic buyer behavior
• Proposes mechanisms ensuring pricing policy robustness across Nash equilibria

Innovation

• Strategy-robust regret notion for strategic buyers
• Polynomial-time approximation scheme using online sketching
• Sparse Update Mechanism ensuring Nash equilibrium robustness