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.

翻译：我们研究了一个在线情境动态定价问题，其中顾客根据产品特征和价格决定是否购买产品。我们提出了一种新颖的建模方法，通过引入基于特征的价格弹性来描述顾客的期望需求，这等价于具有异方差噪声的估值模型。为解决该问题，我们提出了一种计算高效的算法——"扰动定价法 (PwP)"，该算法在允许任意对抗性输入情境序列的条件下，实现了$O(\sqrt{dT\log T})$的遗憾值。同时，我们证明了$\Omega(\sqrt{dT})$的匹配下界，以表明算法在$d$和$T$方面（至多相差$\log T$因子）的最优性。我们的研究揭示了情境弹性与异方差估值之间的内在联系，为制定有效且实用的定价策略提供了理论依据。