Private sequential search and optimization

Abstract

We propose and analyze two models to study an intrinsic trade-off between privacy and query complexity in online settings: 1. Our first private optimization model involves an agent aiming to minimize an objective function expressed as a weighted sum of finitely many convex cost functions, where the weights capture the importance the agent assigns to each cost function. The agent possesses as her private information the weights, but does not know the cost functions, and must obtain information on them by sequentially querying an external data provider. The objective of the agent is to obtain an accurate estimate of the optimal solution, x*, while simultaneously ensuring privacy, by making x* difficult to infer for the data provider, who does not know the agent's private weights but only observes the agent's queries. 2. The second private search model we study is also about protecting privacy while searching for an object. It involves an agent attempting to determine a scalar true value, x*, based on querying an external database, whose response indicates whether the true value is larger than or less than the agent's submitted queries. The objective of the agent is again to obtain an accurate estimate of the true value, x*, while simultaneously hiding it from an adversary who observes the submitted queries but not the responses. The main results of this thesis provide tight upper and lower bounds on the agent's query complexity (i.e., number of queries) as a function of desired levels of accuracy and privacy, for both models. We also explicitly construct query strategies whose worst-case query complexity is optimal up to an additive constant.