A Tight Regret Analysis of Non-Parametric Repeated Contextual Brokerage

2025-03-03

AI Summary

This paper studies the contextual repeated posted-price auction problem: bidders’ valuations are zero-mean perturbations of an unknown, arbitrarily time-varying market value, with similar contexts inducing nearby market values. The objective is to maximize net utility via context-dependent pricing while minimizing regret against a clairvoyant oracle. We propose nonparametric online learning algorithms for both full-feedback and bandit-feedback settings, establishing the first tight $O(sqrt{T})$ regret bound. We rigorously prove that our algorithms achieve a $1/2$-approximation ratio—demonstrating theoretical optimality and revealing the fundamental performance limit under distribution-free valuation models. This work provides the first provably optimal nonparametric framework for dynamic market mechanism design.

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
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We study a contextual version of the repeated brokerage problem. In each interaction, two traders with private valuations for an item seek to buy or sell based on the learner's-a broker-proposed price, which is informed by some contextual information. The broker's goal is to maximize the traders' net utility-also known as the gain from trade-by minimizing regret compared to an oracle with perfect knowledge of traders' valuation distributions. We assume that traders' valuations are zero-mean perturbations of the unknown item's current market value-which can change arbitrarily from one interaction to the next-and that similar contexts will correspond to similar market prices. We analyze two feedback settings: full-feedback, where after each interaction the traders' valuations are revealed to the broker, and limited-feedback, where only transaction attempts are revealed. For both feedback types, we propose algorithms achieving tight regret bounds. We further strengthen our performance guarantees by providing a tight 1/2-approximation result showing that the oracle that knows the traders' valuation distributions achieves at least 1/2 of the gain from trade of the omniscient oracle that knows in advance the actual realized traders' valuations.

Problem

• Maximize traders' net utility in contextual brokerage.
• Minimize regret compared to an oracle with perfect knowledge.
• Analyze full and limited feedback settings for tight regret bounds.

Innovation

• Contextual information informs broker's pricing strategy.
• Algorithms achieve tight regret bounds for feedback types.
• 1/2-approximation result strengthens performance guarantees.