Projection-Free Bandit Optimization with Privacy Guarantees

12/22/2020

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by   Alina Ene, et al.

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We design differentially private algorithms for the bandit convex optimization problem in the projection-free setting. This setting is important whenever the decision set has a complex geometry, and access to it is done efficiently only through a linear optimization oracle, hence Euclidean projections are unavailable (e.g. matroid polytope, submodular base polytope). This is the first differentially-private algorithm for projection-free bandit optimization, and in fact our bound of O(T^3/4) matches the best known non-private projection-free algorithm (Garber-Kretzu, AISTATS `20) and the best known private algorithm, even for the weaker setting when projections are available (Smith-Thakurta, NeurIPS `13).