[论文解读] Differential Privacy in Personalized Pricing with Nonparametric Demand Models

Xi Chen, Sentao Miao+1 more|arXiv (Cornell University)|Sep 10, 2021

Privacy-Preserving Technologies in Data被引用 5

一句话总结

本文提出了两种动态个性化定价算法——CPPQ（适用于中心化差分隐私，CDP）和LPPQ（适用于本地差分隐私，LDP）——在保护客户数据的同时学习非参数化需求模型。该研究建立了近似最优的遗憾边界：CDP下为$\widetilde{O}(T^{(d+2)/(d+4)} + \varepsilon^{-1}T^{d/(d+4)})$，LDP下为$\widetilde{O}(\varepsilon^{-2/(d+2)}T^{(d+1)/(d+2)})$，并通过匹配的下界证明了LDP设置下的近似最优性。

ABSTRACT

In the recent decades, the advance of information technology and abundant personal data facilitate the application of algorithmic personalized pricing. However, this leads to the growing concern of potential violation of privacy due to adversarial attack. To address the privacy issue, this paper studies a dynamic personalized pricing problem with extit{unknown} nonparametric demand models under data privacy protection. Two concepts of data privacy, which have been widely applied in practices, are introduced: extit{central differential privacy (CDP)} and extit{local differential privacy (LDP)}, which is proved to be stronger than CDP in many cases. We develop two algorithms which make pricing decisions and learn the unknown demand on the fly, while satisfying the CDP and LDP gurantees respectively. In particular, for the algorithm with CDP guarantee, the regret is proved to be at most $ ilde O(T^{(d+2)/(d+4)}+\varepsilon^{-1}T^{d/(d+4)})$. Here, the parameter $T$ denotes the length of the time horizon, $d$ is the dimension of the personalized information vector, and the key parameter $\varepsilon>0$ measures the strength of privacy (smaller $\varepsilon$ indicates a stronger privacy protection). On the other hand, for the algorithm with LDP guarantee, its regret is proved to be at most $ ilde O(\varepsilon^{-2/(d+2)}T^{(d+1)/(d+2)})$, which is near-optimal as we prove a lower bound of $Ω(\varepsilon^{-2/(d+2)}T^{(d+1)/(d+2)})$ for any algorithm with LDP guarantee.

研究动机与目标

• 为应对算法个性化定价中因定价决策导致的对抗性推断所引发的隐私泄露问题。
• 设计在线定价算法，在满足正式隐私保障的前提下学习未知的非参数化需求函数。
• 分析在中心化与本地差分隐私下，隐私强度（以$e$衡量）与遗憾性能之间的权衡。
• 建立理论遗憾边界，并证明本地差分隐私设置下的近似最优性。

提出的方法

• 平台采用领域划分策略，将$d$维客户特征空间划分为超立方体，以实现局部价格优化。
• 对于CDP，算法采用基于树的聚合方法来估计测试价格的奖励，并在聚合层级添加拉普拉斯噪声以确保隐私。
• 对于LDP，每个客户的数据在传输前通过注入噪声进行本地化隐私处理，平台则从这些扰动样本中学习需求模型。
• 在每个超立方体内应用一种新颖的四等分搜索方法，以在隐私约束下高效识别近似最优价格。
• 算法使用非参数回归技术，从带有噪声且经过隐私保护的观测中估计未知需求函数。
• 通过集中不等式和在隐私约束下对非参数模型估计误差的界，进行遗憾分析。

Figure 1: CDP (the left panel) and LDP (the right panel) in a general setting.

实验结果

研究问题

• RQ1 在具有非参数需求的动态个性化定价中，隐私强度（$\varepsilon$）与遗憾性能之间的根本权衡是什么？
• RQ2 我们能否设计一种在本地差分隐私（LDP）下实现近似最优遗憾的算法？
• RQ3 当两者均满足正式隐私保障时，基于CDP的定价与基于LDP的定价性能如何比较？
• RQ4 在LDP下可实现的最优遗憾是多少？是否存在一种实用算法能够达到该界限？

主要发现

• 基于CDP的算法（CPPQ）实现了$\widetilde{O}(T^{(d+2)/(d+4)} + \varepsilon^{-1}T^{d/(d+4)})$的遗憾边界，其中第一项与非私有情况下的近似最优边界一致。
• 基于LDP的算法（LPPQ）实现了$\widetilde{O}(\varepsilon^{-2/(d+2)}T^{(d+1)/(d+2)})$的遗憾边界，通过匹配的下界$\Omega(\varepsilon^{-2/(d+2)}T^{(d+1)/(d+2)})$证明了其近似最优性。
• 数值结果证实了遗憾随$T$和$\varepsilon$的理论缩放关系，在LPPQ的对数-对数图中，斜率接近$(d+1)/(d+2)$。
• 对于小$\varepsilon$和中等$T$，尽管LDP提供了更强的隐私保障，LPPQ算法仍可能优于CPPQ，原因在于其噪声缩放更具优势。
• CPPQ的性能对$\varepsilon$极为敏感，遗憾随$\varepsilon^{-1}$增长；而LPPQ的遗憾则按$\varepsilon^{-2/(d+2)}$缩放，对小$\varepsilon$的敏感性较低。

Figure 2: Graphic representation of $\varepsilon$ -CDP. The red and blue arrows mean that two neighboring sequences of data (with the only difference in $s_{j}$ and $s_{j}^{\prime}$ ) are not likely to be distinguished after privatization.