As machine learning (ML) becomes more prevalent in human-centric applications, there is a growing emphasis on algorithmic fairness and privacy protection. While previous research has explored these areas as separate objectives, there is a growing recognition of the complex relationship between privacy and fairness. However, previous works have primarily focused on examining the interplay between privacy and fairness through empirical investigations, with limited attention given to theoretical exploration. This study aims to bridge this gap by introducing a theoretical framework that enables a comprehensive examination of their interrelation. We shall develop and analyze an information bottleneck (IB) based information obfuscation method with local differential privacy (LDP) for fair representation learning. In contrast to many empirical studies on fairness in ML, we show that the incorporation of LDP randomizers during the encoding process can enhance the fairness of the learned representation. Our analysis will demonstrate that the disclosure of sensitive information is constrained by the privacy budget of the LDP randomizer, thereby enabling the optimization process within the IB framework to effectively suppress sensitive information while preserving the desired utility through obfuscation. Based on the proposed method, we further develop a variational representation encoding approach that simultaneously achieves fairness and LDP. Our variational encoding approach offers practical advantages. It is trained using a non-adversarial method and does not require the introduction of any variational prior. Extensive experiments will be presented to validate our theoretical results and demonstrate the ability of our proposed approach to achieve both LDP and fairness while preserving adequate utility.

翻译：随着机器学习在以人为本的应用中日益普及，算法公平性与隐私保护受到越来越多的关注。尽管以往研究将这两个目标分开探讨，但人们逐渐认识到隐私与公平之间复杂的关联性。然而，现有工作主要依赖实证研究考察隐私与公平的相互作用，对理论探索的关注有限。本研究旨在通过构建一个综合性理论框架来弥补这一差距，从而系统探究二者的内在联系。我们将开发并分析一种基于信息瓶颈的、结合本地差分隐私的信息混淆方法，用于公平表示学习。与许多关于机器学习公平性的实证研究不同，我们证明在编码过程中引入本地差分隐私随机化器能够增强所学表示的公平性。我们的分析将表明，敏感信息的泄露受限于本地差分隐私随机化器的隐私预算，这使得信息瓶颈框架内的优化过程能够有效抑制敏感信息，同时通过混淆手段保留所需的效用。基于所提方法，我们进一步开发了一种变分表示编码方法，可同时实现公平性与本地差分隐私。该变分编码方法具有实际优势：它采用非对抗性训练，无需引入任何变分先验。我们将通过大量实验验证理论结果，并证明所提方法能在保持充分效用的同时实现本地差分隐私与公平性。