Private Sequential Learning

We formulate a private learning model to study an intrinsic tradeoff between privacy and query complexity in sequential learning. Our model involves a learner who aims to determine a scalar value $v^{\mathrm{\ast }}$ by sequentially querying an external database and receiving binary responses. In the meantime, an adversary observes the learner’s queries, although not the responses, and tries to infer from them the value of $v^{\mathrm{\ast }}$. The objective of the learner is to obtain an accurate estimate of $v^{\mathrm{\ast }}$ using only a small number of queries while simultaneously protecting his or her privacy by making $v^{\mathrm{\ast }}$ provably difficult to learn for the adversary. Our main results provide tight upper and lower bounds on the learner’s query complexity as a function of desired levels of privacy and estimation accuracy. We also construct explicit query strategies whose complexity is optimal up to an additive constant.