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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 decisionspublicly, which may breach our privacy - a party observing our choices maylearn a lot about our preferences. In this paper we investigate the onlinestopping algorithms from the privacy preserving perspective, using amathematically rigorous differential privacy notion. In differentially privatealgorithms there is usually an issue of balancing the privacy and utility. Inthis regime, in most cases, having both optimality and high level of privacy atthe same time is impossible. We propose a natural mechanism to achieve acontrollable trade-off, quantified by a parameter, between the accuracy of theonline algorithm and its privacy. Depending on the parameter, our mechanism canbe optimal with weaker differential privacy or suboptimal, yet moreprivacy-preserving. We conduct a detailed accuracy and privacy analysis of ourmechanism applied to the optimal algorithm for the classical secretary problem.Thereby the classical notions from two distinct areas - optimal stopping anddifferential privacy - meet for the first time.

What Do Our Choices Say About Our Preferences?