On the Optimal Regret of Locally Private Linear Contextual Bandit
This solves an open problem in privacy-preserving online learning, enabling efficient learning with strong privacy guarantees for applications handling sensitive user data.
The paper tackles the problem of achieving optimal regret in locally private linear contextual bandit learning, where sensitive data must be protected, and shows that it is possible to attain an $ ilde O(\sqrt{T})$ regret upper bound, matching the classical non-private case.
Contextual bandit with linear reward functions is among one of the most extensively studied models in bandit and online learning research. Recently, there has been increasing interest in designing \emph{locally private} linear contextual bandit algorithms, where sensitive information contained in contexts and rewards is protected against leakage to the general public. While the classical linear contextual bandit algorithm admits cumulative regret upper bounds of $\tilde O(\sqrt{T})$ via multiple alternative methods, it has remained open whether such regret bounds are attainable in the presence of local privacy constraints, with the state-of-the-art result being $\tilde O(T^{3/4})$. In this paper, we show that it is indeed possible to achieve an $\tilde O(\sqrt{T})$ regret upper bound for locally private linear contextual bandit. Our solution relies on several new algorithmic and analytical ideas, such as the analysis of mean absolute deviation errors and layered principal component regression in order to achieve small mean absolute deviation errors.