在资源有限下优化动态定价，三种算法适配不同信息条件。
Learning to Price with Resource Constraints: From Full Information to Machine-Learned Prices
- 针对不同信息水平设计三类定价算法，兼顾探索与利用。
- 全信息下算法实现对数级后悔值，无非退化条件要求。
- 可利用预训练价格提升性能，适合有历史数据的场景。
我们研究带有背包约束的动态定价问题，解决资源受限下探索与利用的平衡挑战。提出三种适配不同信息设置的算法：全信息下的边界吸引重求解方法、无先验信息下的在线学习算法，以及利用机器学习估计价格且已知误差上界的估价-选择重求解算法。边界吸引重求解方法在无需非退化条件的情况下实现对数级后悔；在线学习算法达到最优的 $O( )$ 回悔。估价-选择方法弥合了两者差距，在可靠离线数据可用时提供更优的后悔界。数值实验验证了算法在多种场景下的有效性和鲁棒性。本工作推进了对在线资源分配与动态定价的理解，提供了可适配不同信息结构的实际解决方案。
原文摘要 · Abstract (English)
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.
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