用贝叶斯优化动态定价，无需假设需求函数形式

Dynamic pricing is the practice of adjusting the selling price of a product to maximize a firm's revenue by responding to market demand. The literature typically distinguishes between two settings: infinite inventory, where the firm has unlimited stock and time to sell, and finite inventory, where both inventory and selling horizon are limited. In both cases, the central challenge lies in the fact that the demand function -- how sales respond to price -- is unknown and must be learned from data. Traditional approaches often assume a specific parametric form for the demand function, enabling the use of reinforcement learning (RL) to identify near-optimal pricing strategies. However, such assumptions may not hold in real-world scenarios, limiting the applicability of these methods. In this work, we propose a Gaussian Process (GP) based nonparametric approach to dynamic pricing that avoids restrictive modeling assumptions. We treat the demand function as a black-box function of the price and develop pricing algorithms based on Bayesian Optimization (BO) -- a sample-efficient method for optimizing unknown functions. We present BO-based algorithms tailored for both infinite and finite inventory settings and provide regret guarantees for both regimes, thereby quantifying the learning efficiency of our methods. Through extensive experiments, we demonstrate that our BO-based methods outperform several state-of-the-art RL algorithms in terms of revenue, while requiring fewer assumptions and offering greater robustness. This highlights Bayesian Optimization as a powerful and practical tool for dynamic pricing in complex, uncertain environments.