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 γ, proving that our algorithm achieves a regret upper bound of O(T (1+γ)/2 + √ dT ) for γ < 1/3 and O(T 2/3 + √ dT ) for γ ≥ 1/3, where γ 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.