Multi-Product Dynamic Pricing in High-Dimensions with Heterogenous Price Sensitivity

We consider the problem of multi-product dynamic pricing in a contextual setting for a seller of differentiated products. In this environment, the customers arrive over time and products are described by high-dimensional feature vectors. Each customer chooses a product according to the widely used Multinomial Logit (MNL) choice model and her utility depends on the product features as well as the prices offered. Our model allows for heterogenous price sensitivities for products. The seller a-priori does not know the parameters of the choice model but can learn them through interactions with the customers. The seller's goal is to design a pricing policy that maximizes her cumulative revenue. This model is motivated by online marketplaces such as Airbnb platform and online advertising. We measure the performance of a pricing policy in terms of regret, which is the expected revenue loss with respect to a clairvoyant policy that knows the parameters of the choice model in advance and always sets the revenue-maximizing prices. We propose a pricing policy, named M3P, that achieves a $T$-period regret of $O(\sqrt{\log(dT) T})$ under heterogenous price sensitivity for products with features dimension of $d$. We also prove that no policy can achieve worst-case $T$-regret better than $\Omega(\sqrt{T})$.