  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.
