让定价模型既透明又高效，直接看属性如何影响价格。
Learning to Price: Interpretable Attribute-Level Models for Dynamic Markets
- 用属性分解建模，把价格拆成各属性贡献之和。
- 在线学习算法在动态市场中实现近最优定价，误差随时间增长缓慢。
- 适合需要解释性与快速响应的电商、零售等场景。
高维市场中的动态定价面临可扩展性、不确定性与可解释性的根本挑战。现有低秩带宽方法虽高效，但依赖难以理解的隐式特征，无法揭示单个产品属性对价格的影响。为此，我们提出可解释的**属性级分解低维需求（AFDLD）模型**，将产品价格表示为属性贡献之和，并显式建模替代效应。基于此结构，我们设计了**ADEPT**（属性分解定价算法，支持交叉弹性与时间自适应学习）——一种无需投影、无梯度的在线学习算法，在属性空间直接运行，达到$ ilde{ ext{O}}( ext{√d}T^{3/4})$的次线性后悔率。通过受控合成实验与真实数据集验证，ADEPT（i）在动态市场下学习接近最优的价格，（ii）能快速适应外部冲击与趋势漂移，（iii）提供清晰的属性级定价解释。结果表明，通过结构化属性驱动表示，可同时实现自主定价代理的可解释性与效率。
原文摘要 · Abstract (English)
Dynamic pricing in high-dimensional markets poses fundamental challenges of scalability, uncertainty, and interpretability. Existing low-rank bandit formulations learn efficiently but rely on latent features that obscure how individual product attributes influence price. We address this by introducing an interpretable \emph{Additive Feature Decomposition-based Low-Dimensional Demand (\textbf{AFDLD}) model}, where product prices are expressed as the sum of attribute-level contributions and substitution effects are explicitly modeled. Building on this structure, we propose \textbf{ADEPT} (Additive DEcomposition for Pricing with cross-elasticity and Time-adaptive learning)-a projection-free, gradient-free online learning algorithm that operates directly in attribute space and achieves a sublinear regret of $\tilde{\mathcal{O}}(\sqrt{d}T^{3/4})$. Through controlled synthetic studies and real-world datasets, we show that ADEPT (i) learns near-optimal prices under dynamic market conditions, (ii) adapts rapidly to shocks and drifts, and (iii) yields transparent, attribute-level price explanations. The results demonstrate that interpretability and efficiency in autonomous pricing agents can be achieved jointly through structured, attribute-driven representations.
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