跨市场联合定价与商品组合的迁移学习方法,能有效应对顾客偏好差异。
Transfer Learning for Contextual Joint Assortment-Pricing under Cross-Market Heterogeneity
- 基于结构化效用偏移建模跨市场差异,分离共享与异质偏好方向。
- 理论证明算法在连续价格下可实现最优后悔上界,加速学习并控制偏差。
- 适合多市场运营且面临用户偏好差异的电商、零售平台使用。
研究在多重日志选择模型和贝叶斯反馈下,跨市场情境中的联合商品组合与定价迁移学习问题。卖家在多个相关市场运营,仅观测到报价和实际购买行为。虽然源市场的数据可加速目标市场的学习,但客户偏好的跨市场差异若未经处理,可能引入系统性偏差。本文通过结构化效用偏移建模异质性:各市场共享相同的上下文效用结构,但在少数隐含偏好维度上存在差异。基于此,提出偏差感知框架TJAP,结合聚合-去偏估计与UCB型策略。TJAP构建双半径置信区间,分别捕捉统计不确定性和迁移带来的偏差,统一覆盖连续价格空间。理论推导出匹配的极小极大后悔上界: $\tilde{O}\! \left(d\sqrt{\frac{T}{1+H}} + s_0\sqrt{T}\right)$,揭示清晰的方差-偏差权衡:迁移加速共享偏好方向的学习,而异质成分带来不可消除的适应成本。数值实验验证理论结果,表明TJAP优于仅依赖目标市场学习或简单数据合并的方法,且对跨市场差异保持鲁棒。
原文摘要 · Abstract (English)
We study transfer learning for contextual joint assortment-pricing under a multinomial logit choice model with bandit feedback. A seller operates across multiple related markets and observes only posted prices and realized purchases. While data from source markets can accelerate learning in a target market, cross-market differences in customer preferences may introduce systematic bias if pooled indiscriminately. We model heterogeneity through a structured utility shift, where markets share a common contextual utility structure but differ along a sparse set of latent preference coordinates. Building on this, we develop Transfer Joint Assortment-Pricing (TJAP), a bias-aware framework that combines aggregate-then-debias estimation with a UCB-style policy. TJAP constructs two-radius confidence bounds that separately capture statistical uncertainty and transfer-induced bias, uniformly over continuous prices. We establish matching minimax regret bounds of order $\tilde{O}\!\left(d\sqrt{\frac{T}{1+H}} + s_0\sqrt{T}\right),$revealing a transparent variance-bias tradeoff: transfer accelerates learning along shared preference directions, while heterogeneous components impose an irreducible adaptation cost. Numerical experiments corroborate the theory, showing that TJAP outperforms both target-only learning and naive pooling while remaining robust to cross-market differences.
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