Pricing with Contextual Elasticity and Heteroscedastic Valuation

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(√dTlog T) regret while allowing arbitrary adversarial input context sequences. We also prove a matching lower bound at Omega(√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.