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We study the query complexity of a learner-private sequential learningproblem, motivated by the privacy and security concerns due to eavesdroppingthat arise in practical applications such as pricing and Federated Learning. Alearner tries to estimate an unknown scalar value, by sequentially querying anexternal database and receiving binary responses; meanwhile, a third-partyadversary observes the learner's queries but not the responses. The learner'sgoal is to design a querying strategy with the minimum number of queries(optimal query complexity) so that she can accurately estimate the true value,while the eavesdropping adversary even with the complete knowledge of herquerying strategy cannot.  We develop new querying strategies and analytical techniques and use them toprove tight upper and lower bounds on the optimal query complexity. The boundsalmost match across the entire parameter range, substantially improving uponexisting results. We thus obtain a complete picture of the optimal querycomplexity as a function of the estimation accuracy and the desired levels ofprivacy. We also extend the results to sequential learning models in higherdimensions, and where the binary responses are noisy. Our analysis leverages acrucial insight into the nature of private learning problem, which suggeststhat the query trajectory of an optimal learner can be divided into distinctphases that focus on pure learning versus learning and obfuscation,respectively.

Optimal query complexity for private sequential learning against eavesdropping