We study an online contextual dynamic pricing problem, where customers decide
whether to purchase a product based on its features and price. We introduce a
novel approach to modeling a customer's expected demand by incorporating
feature-based price elasticity, which can be equivalently represented as a
valuation with heteroscedastic noise. To solve the problem, we propose a
computationally efficient algorithm called "Pricing with Perturbation (PwP)",
which enjoys an $O(\sqrt{dT\log T})$ regret while allowing arbitrary
adversarial input context sequences. We also prove a matching lower bound at
$\Omega(\sqrt{dT})$ to show the optimality regarding $d$ and $T$ (up to $\log
T$ factors). Our results shed light on the relationship between contextual
elasticity and heteroscedastic valuation, providing insights for effective and
practical pricing strategies.

我们研究了一种在线上下文动态定价问题，介绍了一种以特征为基础的价格弹性建模方法，提出了一种高效的算法 “Pricing with Perturbation (PwP)”，并证明了其在任意敌对背景输入序列下的最佳性及相应的复杂度。该研究结果揭示了上下文弹性与异方差性估价之间的关系，为有效和实用的定价策略提供了启示。