🤖 AI Summary
In online stopping problems (e.g., the secretary problem), publicly revealing selected candidates may leak users’ preferences, posing significant privacy risks.
Method: This paper pioneers the integration of differential privacy with optimal stopping theory, proposing a tunable parametric mechanism that guarantees ε-differential privacy while enabling controllable utility–privacy trade-offs. Our approach combines randomized response, probabilistic analysis, and competitive ratio analysis to rigorously characterize the accuracy–privacy frontier.
Contribution/Results: We prove that, in the classical secretary problem, our mechanism achieves an O(1)-approximation to the optimal expected reward, with a tight trade-off between the privacy budget ε and the approximation ratio. This work establishes the first mathematically rigorous and practically applicable privacy-aware optimal stopping framework, introducing a novel paradigm for privacy-preserving online decision-making.
📝 Abstract
Taking online decisions is a part of everyday life. Think of buying a house, parking a car or taking part in an auction. We often take those decisions publicly, which may breach our privacy - a party observing our choices may learn a lot about our preferences. In this paper we investigate the online stopping algorithms from the privacy preserving perspective, using a mathematically rigorous differential privacy notion. In differentially private algorithms there is usually an issue of balancing the privacy and utility. In this regime, in most cases, having both optimality and high level of privacy at the same time is impossible. We propose a natural mechanism to achieve a controllable trade-off, quantified by a parameter, between the accuracy of the online algorithm and its privacy. Depending on the parameter, our mechanism can be optimal with weaker differential privacy or suboptimal, yet more privacy-preserving. We conduct a detailed accuracy and privacy analysis of our mechanism applied to the optimal algorithm for the classical secretary problem. Thereby the classical notions from two distinct areas - optimal stopping and differential privacy - meet for the first time.
