Dynamic pricing, the practice of adjusting prices based on contextual
factors, has gained significant attention due to its impact on revenue
maximization. In this paper, we address the contextual dynamic pricing problem,
which involves pricing decisions based on observable product features and
customer characteristics. We propose a novel algorithm that achieves improved
regret bounds while minimizing assumptions about the problem. Our algorithm
discretizes the unknown noise distribution and combines the upper confidence
bounds with a layered data partitioning technique to effectively regulate
regret in each episode. These techniques effectively control the regret
associated with pricing decisions, leading to the minimax optimality.
Specifically, our algorithm achieves a regret upper bound of
$\tilde{\mathcal{O}}(\rho_{\mathcal{V}}^{\frac{1}{3}}(\delta)
T^{\frac{2}{3}})$, where $\rho_{\mathcal{V}}(\delta)$ represents the estimation
error of the valuation function. Importantly, this bound matches the lower
bound up to logarithmic terms, demonstrating the minimax optimality of our
approach. Furthermore, our method extends beyond linear valuation models
commonly used in dynamic pricing by considering general function spaces. We
simplify the estimation process by reducing it to general offline regression
oracles, making implementation more straightforward.

通过可观察的产品特征和顾客特征，提出一种新算法，通过离散化未知噪声分布和上限置信区间与分层数据分区技术的组合，有效地调节每个周期中的懊悔，从而控制与定价决策相关的懊悔，实现极小极大优化。