Semi-Parametric Contextual Pricing Algorithm using Cox Proportional Hazards Model

Contextual dynamic pricing is a problem of setting prices based on current contextual information and previous sales history to maximize revenue. A popular approach is to postulate a distribution of customer valuation as a function of contextual information and the baseline valuation. A semi-parametric setting, where the context effect is parametric and the baseline is nonparametric, is of growing interest due to its flexibility. A challenge is that customer valuation is almost never observable in practice and is instead type-I interval censored by the offered price. To address this challenge, we propose a novel semi-parametric contextual pricing algorithm for stochastic contexts, called the epoch-based Cox proportional hazards Contextual Pricing (CoxCP) algorithm. To our best knowledge, our work is the first to employ the Cox model for customer valuation. The CoxCP algorithm has a high-probability regret upper bound of Õ(T 2 3 d), where T is the length of horizon and d is the dimension of context. In addition, if the baseline is known, the regret bound can improve to O(d log T ) under certain assumptions. We demonstrate empirically the proposed algorithm performs better than existing semi-parametric contextual pricing algorithms when the model assumptions of all algorithms are correct.