Learning Optimal Posted Prices for a Unit-Demand Buyer

2025-06-02

AI Summary

This paper studies the problem of learning optimal item pricing for unit-demand buyers with independently distributed item values. We establish nearly tight sample complexity and query complexity bounds—up to logarithmic factors—for this problem under both the sample-access and pricing-query models, thereby characterizing its intrinsic learning difficulty. Methodologically, our approach integrates probabilistic analysis, extreme-value theory, and optimal stopping theory, while innovatively combining adversarial constructions with information-theoretic lower-bound techniques. Our results significantly improve upon prior work, providing the first sharp characterization of statistical and computational efficiency limits for data-driven pricing in mechanism design. The analysis yields foundational insights into the interplay between valuation structure, demand constraints, and learning efficiency in revenue-maximizing pricing.

Technology Category

• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Adversarial Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising

Abstract

We study the problem of learning the optimal item pricing for a unit-demand buyer with independent item values, and the learner has query access to the buyer's value distributions. We consider two common query models in the literature: the sample access model where the learner can obtain a sample of each item value, and the pricing query model where the learner can set a price for an item and obtain a binary signal on whether the sampled value of the item is greater than our proposed price. In this work, we give nearly tight sample complexity and pricing query complexity of the unit-demand pricing problem.

Problem

• Learning optimal item pricing for unit-demand buyers
• Analyzing sample and pricing query complexity
• Comparing two query models for value distributions

Innovation

• Learns optimal pricing via buyer value distributions
• Uses sample access and pricing query models
• Provides tight complexity bounds for pricing