跨市场迁移定价算法，让价格策略学得更快更准。
Transfer Faster, Price Smarter: Minimax Dynamic Pricing under Cross-Market Preference Shift
- 利用多个辅助市场的数据，自动适应目标市场的偏好变化。
- 线性模型下误差随市场数量增加而降低，非线性模型也达理论最优。
- 适合需要快速适应新市场的电商、平台等实时定价场景。
我们研究在目标市场可借助 K 个辅助市场（离线日志或实时流）进行上下文动态定价的问题，这些辅助市场的均值效用存在结构化偏好偏移。提出首个能严格处理此类模型偏移迁移的算法——跨市场迁移动态定价（CM-TDP），在线性和非参数效用模型下均实现极小极大最优后悔值。对于维度为 d、系数差异为 s₀-稀疏的线性效用，其后悔值为 Õ((d*K⁻¹ + s₀) log T)；对于位于再生核希尔伯特空间（RKHS）中、有效维度为 α、复杂度为 β、任务相似性参数为 H 的非线性需求，后悔值为 Õ(K⁻²αβ/(2αβ+1) T¹/(2αβ+1) + H²/(2α+1) T¹/(2α+1))，逼近信息论下界。该 RKHS 结果是首个适用于迁移定价的，具有独立价值。大量模拟显示，相比单市场基准，累计后悔降低高达 50%，学习速度提升 5 倍。
原文摘要 · Abstract (English)
We study contextual dynamic pricing when a target market can leverage K auxiliary markets -- offline logs or concurrent streams -- whose mean utilities differ by a structured preference shift. We propose Cross-Market Transfer Dynamic Pricing (CM-TDP), the first algorithm that provably handles such model-shift transfer and delivers minimax-optimal regret for both linear and non-parametric utility models. For linear utilities of dimension d, where the difference between source- and target-task coefficients is $s_{0}$-sparse, CM-TDP attains regret $\tilde{O}((d*K^{-1}+s_{0})\log T)$. For nonlinear demand residing in a reproducing kernel Hilbert space with effective dimension $α$, complexity $β$ and task-similarity parameter $H$, the regret becomes $\tilde{O}\!(K^{-2αβ/(2αβ+1)}T^{1/(2αβ+1)} + H^{2/(2α+1)}T^{1/(2α+1)})$, matching information-theoretic lower bounds up to logarithmic factors. The RKHS bound is the first of its kind for transfer pricing and is of independent interest. Extensive simulations show up to 50% lower cumulative regret and 5 times faster learning relative to single-market pricing baselines. By bridging transfer learning, robust aggregation, and revenue optimization, CM-TDP moves toward pricing systems that transfer faster, price smarter.
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