Pricing with Contextual Elasticity and Heteroscedastic Valuation
This work addresses pricing strategies for businesses by providing optimal algorithms with theoretical guarantees, though it is incremental in refining existing models.
The paper tackles the online contextual dynamic pricing problem by modeling customer demand with feature-based price elasticity, equivalent to heteroscedastic valuation, and proposes the Pricing with Perturbation (PwP) algorithm achieving O(√(dT log T)) regret with adversarial contexts, along with a matching lower bound of Ω(√(dT)).
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 $Ω(\sqrt{dT})$ 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.