Learning to Price with Resource Constraints: From Full Information to Machine-Learned Prices

TL;DR

This paper develops algorithms for dynamic pricing under resource constraints, effectively balancing exploration and exploitation across different informational settings, with proven regret bounds and practical validation.

Contribution

It introduces three novel algorithms for resource-constrained dynamic pricing, including a full-information method, an online learning approach, and an estimate-then-select strategy leveraging machine learning.

Findings

Boundary Attracted Re-solve achieves logarithmic regret.

Online learning algorithm attains optimal $O(\

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Abstract

We study the dynamic pricing problem with knapsack, addressing the challenge of balancing exploration and exploitation under resource constraints. We introduce three algorithms tailored to different informational settings: a Boundary Attracted Re-solve Method for full information, an online learning algorithm for scenarios with no prior information, and an estimate-then-select re-solve algorithm that leverages machine-learned informed prices with known upper bound of estimation errors. The Boundary Attracted Re-solve Method achieves logarithmic regret without requiring the non-degeneracy condition, while the online learning algorithm attains an optimal $O(\sqrt{T})$ regret. Our estimate-then-select approach bridges the gap between these settings, providing improved regret bounds when reliable offline data is available. Numerical experiments validate the effectiveness and robustness of our algorithms across various scenarios. This work advances the understanding of online resource allocation and dynamic pricing, offering practical solutions adaptable to different informational structures.