A Bayesian Approach to Contextual Dynamic Pricing using the Proportional Hazards Model with Discrete Price Data

Dynamic pricing algorithms typically assume continuous price variables, which may not reflect real-world scenarios where prices are often discrete. This paper demonstrates that leveraging discrete price information within a semi-parametric model can substantially improve performance, depending on the size of the support set of the price variable relative to the time horizon.

Specifically, we propose a novel semi-parametric contextual dynamic pricing algorithm, namely BayesCoxCP, based on a Bayesian approach to the Cox proportional hazards model.

Our theoretical analysis establishes high-probability regret bounds that adapt to the sparsity level $\gamma$, proving that our algorithm achieves a regret upper bound of $O(T^{(1+\gamma )/2}+\sqrt{dT})$ for $\gamma <1/3$ and $O(T^{2/3}+\sqrt{dT})$ for $\gamma \ge 1/3$, where $\gamma$ represents the sparsity of the price grid relative to the time horizon $T$.

Through numerical experiments, we demonstrate that our proposed algorithm significantly outperforms an existing method, particularly in scenarios with sparse discrete price points.