Contextual bandit algorithms are useful in personalized online decision-making. However, many applications such as personalized medicine and online advertising require the utilization of individual-specific information for effective learning, while user's data should remain private from the server due to privacy concerns. This motivates the introduction of local differential privacy (LDP), a stringent notion in privacy, to contextual bandits. In this paper, we design LDP algorithms for stochastic generalized linear bandits to achieve the same regret bound as in non-privacy settings. Our main idea is to develop a stochastic gradient-based estimator and update mechanism to ensure LDP. We then exploit the flexibility of stochastic gradient descent (SGD), whose theoretical guarantee for bandit problems is rarely explored, in dealing with generalized linear bandits. We also develop an estimator and update mechanism based on Ordinary Least Square (OLS) for linear bandits. Finally, we conduct experiments with both simulation and real-world datasets to demonstrate the consistently superb performance of our algorithms under LDP constraints with reasonably small parameters $(\varepsilon, \delta)$ to ensure strong privacy protection.

本文介绍了使用本地差分隐私的情境赌博算法，为了在保持用户数据隐私不受侵犯的情况下个性化学习，利用了一种基于随机梯度下降法的估计器和更新机制来确保使用LDP，并且在广义线性情境中利用了该方法。我们还开发了一个基于最小二乘法的评估器和更新机制，最后通过模拟和实际数据集的实验来证明了算法的性能在强隐私保护的条件下具有相当好的表现。

具有本地差分隐私的广义线性赌博机