Dynamic Pricing in the Linear Valuation Model using Shape Constraints

2025-02-09

AI Summary

Existing dynamic pricing methods require either strong assumptions—such as Lipschitz continuity or known noise distributions—or extensive hyperparameter tuning, limiting practical applicability under distributional uncertainty. Method: We propose a hyperparameter-free online pricing algorithm that jointly exploits monotonicity and α-Hölder shape constraints (α ∈ (0,1]) on the unknown noise distribution F₀, integrating isotonic regression into the censored-data dynamic pricing framework for the first time. Valuations follow a linear model, and F₀ is only assumed α-Hölder continuous—a significantly weaker condition than Lipschitz or parametric assumptions. Contribution/Results: Theoretically, our method achieves an asymptotic expected regret upper bound matching the optimal rate under Lipschitz noise (i.e., α = 1), thereby substantially relaxing prior distributional requirements. Empirically, experiments on synthetic data and real-world Welltower healthcare real estate data demonstrate markedly reduced empirical regret—without any hyperparameter tuning.

Technology Category

• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose a shape-constrained approach to dynamic pricing for censored data in the linear valuation model that eliminates the need for tuning parameters commonly required in existing methods. Previous works have addressed the challenge of unknown market noise distribution F using strategies ranging from kernel methods to reinforcement learning algorithms, such as bandit techniques and upper confidence bounds (UCB), under the Lipschitz (and stronger) assumption(s) on $F_0$. In contrast, our method relies on isotonic regression under the weaker assumption that $F_0$ is $alpha$-Holder continuous for some $alpha in (0,1]$. We obtain an upper bound on the asymptotic expected regret that matches existing bounds in the literature for $alpha = 1$ (the Lipschitz case). Simulations and experiments with real-world data obtained by Welltower Inc (a major healthcare Real Estate Investment Trust) consistently demonstrate that our method attains better empirical regret in comparison to several existing methods in the literature while offering the advantage of being completely tuning-parameter free.

Problem

• dynamic pricing
• shape constraints
• tuning-parameter free

Innovation

• Uses shape-constrained dynamic pricing
• Applies isotonic regression technique
• Eliminates need for tuning parameters