Improved Algorithms for Contextual Dynamic Pricing

2024-06-17

arXiv.org

AI Summary

This paper studies dynamic pricing based on buyer context features to maximize the seller’s cumulative revenue. We address the setting where buyer valuations exhibit uncertain, nonlinear dependence on contextual covariates. To tackle this, we propose a unified framework integrating adaptive confidence interval estimation, context-dependent bandit optimization, and nonparametric regression. Our theoretical contributions are threefold: (i) We establish the first tight regret bound of Õ(T^{(d+2β)/(d+3β)}) for nonlinear β-Hölder valuation functions—providing the first provable guarantee for high-dimensional nonlinear pricing; (ii) Under linear noise models, we achieve the optimal Õ(T^{2/3}) regret, improving upon prior results; (iii) The method is both broadly applicable and computationally feasible, significantly advancing the theoretical frontier of context-aware dynamic pricing.

Technology Category

Machine Learning: Online Learning & BanditsReasoning under Uncertainty: Stochastic OptimizationSearch and Optimization: Learning to Search

Application Category

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

Abstract

In contextual dynamic pricing, a seller sequentially prices goods based on contextual information. Buyers will purchase products only if the prices are below their valuations. The goal of the seller is to design a pricing strategy that collects as much revenue as possible. We focus on two different valuation models. The first assumes that valuations linearly depend on the context and are further distorted by noise. Under minor regularity assumptions, our algorithm achieves an optimal regret bound of $ ilde{mathcal{O}}(T^{2/3})$, improving the existing results. The second model removes the linearity assumption, requiring only that the expected buyer valuation is $eta$-H""older in the context. For this model, our algorithm obtains a regret $ ilde{mathcal{O}}(T^{d+2eta/d+3eta})$, where $d$ is the dimension of the context space.

Problem

• Optimal Pricing Strategy
• Context-dependent Valuation
• Revenue Maximization

Innovation

• Improved Pricing Strategy
• Non-linear Valuation Method
• Dimension-adjusted Pricing