Dynamic Pricing in the Linear Valuation Model using Shape Constraints
This work addresses the problem of dynamic pricing for companies, such as Real Estate Investment Trusts, that need to optimize their pricing strategies, offering an incremental improvement over existing methods.
The authors tackled the problem of dynamic pricing in the linear valuation model with censored data, achieving lower empirical regret compared to existing methods, with a regret upper bound derived under the assumption of α-Hölder continuity. Their method attained better results in simulations and real-world experiments with no need for tuning parameters.
We propose a shape-constrained approach to dynamic pricing for censored data in the linear valuation model eliminating the need for tuning parameters commonly required by existing methods. Previous works have addressed the challenge of unknown market noise distribution $F_0$ using strategies ranging from kernel methods to reinforcement learning algorithms, such as bandit techniques and upper confidence bounds (UCB), under the assumption that $F_0$ satisfies Lipschitz (or stronger) conditions. In contrast, our method relies on isotonic regression under the weaker assumption that $F_0$ is $α$-Hölder continuous for some $α\in (0,1]$, for which we derive a regret upper bound. Simulations and experiments with real-world data obtained by Welltower Inc (a major healthcare Real Estate Investment Trust) consistently demonstrate that our method attains lower empirical regret in comparison to several existing methods in the literature while offering the advantage of being tuning-parameter free.