  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, $v^*$, by sequentially querying
an external database and receiving binary responses. In the meantime, an
adversary observes the learner's queries, though not the responses, and tries
to infer from them the value of $v^*$. The objective of the learner is to
obtain an accurate estimate of $v^*$ using only a small number of queries,
while simultaneously protecting her privacy by making $v^*$ 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.
