In collaborative recommendation systems, privacy may be compromised, as
users' opinions are used to generate recommendations for others. In this paper,
we consider an online collaborative recommendation system, and we measure
users' privacy in terms of the standard differential privacy. We give the first
quantitative analysis of the trade-offs between recommendation quality and
users' privacy in such a system by showing a lower bound on the best achievable
privacy for any non-trivial algorithm, and proposing a near-optimal algorithm.
From our results, we find that there is actually little trade-off between
recommendation quality and privacy for any non-trivial algorithm. Our results
also identify the key parameters that determine the best achievable privacy.