Privacy-Preserving Personalized Recommender Systems

Although personalized recommender systems are vital for many online platforms, they lead to controversial societal issues such as privacy breaches. In response to such concerns, there is a clear regulatory trend in calling for stringent privacy protection mechanisms implanted in such algorithms. In this work, we study the optimal design of a personalized recommender system with the local differential privacy constraints imposed by some external regulators. The recommender system recommends a product to a consumer based on her preference ranking of products, potentially learned from her personal data such as cookies. The differential privacy impedes inferring the consumer's sensitive information from the recommendation outcome. We show the optimal recommendation policy is a coarse-grained threshold policy: it randomly selects a product to recommend with a subset having higher recommendation probabilities than the rest, where the subset is determined by a threshold on the consumer's preference ranking. We analyze the choice of the threshold and the randomized recommendation in the asymptotic regime with a large number of products, relevant to most online platforms. Our analysis further suggests that pursuing privacy is not a free lunch: it comes at a substantial economic loss due to the resulting inaccurate recommendation, although it may benefit consumers monetarily via the induced lower product price associated with the less relevant recommendation. Taken together, our study provides guidance for practitioners regarding the design of privacy-preserving personalized recommendation algorithms and discusses the implications of the privacy policy for regulators.