高精度预测可让稀缺资源定价从随机波动转为稳定优化
The Value of Information in Resource-Constrained Pricing
- 用带误差边界的预测确定最优定价区间
- 当预测误差小于T^{-1/4}时,后悔值从O(√T)降至O(log T)
- 替代模型通过协变量降低学习方差,适合数据有限场景
针对航空座位、酒店房间等易逝性资源的动态定价问题,研究在容量有限、需求线性且存在随机噪声的条件下,预测不确定性如何影响定价决策。已知误差上界ε^0的可信预测可将后悔值从O(√T)降至O(log T),当ε^0 ≲ T^{-1/4}时该阈值紧致。使用有偏但与真实需求相关联的替代模型(ρ²为相关系数)可通过协变量方法将学习方差降低(1−ρ²)倍。两种机制协同:预测决定后悔率阶段,替代模型优化该阶段内的估计精度。所有算法基于边界吸引机制,在无需非退化假设下稳定定价于容量边界附近。实验验证了相变阈值、方差降低效果及跨实例鲁棒性。
原文摘要 · Abstract (English)
Firms that price perishable resources -- airline seats, hotel rooms, seasonal inventory -- now routinely use demand predictions, but these predictions vary widely in quality. Under hard capacity constraints, acting on an inaccurate prediction can irreversibly deplete inventory needed for future periods. We study how prediction uncertainty propagates into dynamic pricing decisions with linear demand, stochastic noise, and finite capacity. A certified demand forecast with known error bound~$ε^0$ specifies where the system should operate: it shifts regret from $O(\sqrt{T})$ to $O(\log T)$ when $ε^0 \lesssim T^{-1/4}$, and we prove this threshold is tight. A misspecified surrogate model -- biased but correlated with true demand -- cannot set prices directly but reduces learning variance by a factor of $(1-ρ^2)$ through control variates. The two mechanisms compose: the forecast determines the regret regime; the surrogate tightens estimation within it. All algorithms rest on a boundary attraction mechanism that stabilizes pricing near degenerate capacity boundaries without requiring non-degeneracy assumptions. Experiments confirm the phase transition threshold, the variance reduction from surrogates, and robustness across problem instances.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。