Projection-Free Bandit Optimization with Privacy Guarantees

• URL: http://arxiv.org/abs/2012.12138v1
• Date: Tue, 22 Dec 2020 16:19:29 GMT
• Title: Projection-Free Bandit Optimization with Privacy Guarantees
• Authors: Alina Ene, Huy L. Nguyen, Adrian Vladu
• Abstract summary: 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. This is the first differentially-private algorithm for projection-free bandit optimization, and in fact our bound of $widetildeO(T3/4)$ matches the best known non-private projection-free algorithm.
• Score: 18.95253453749389
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\widetilde{O}(T^{3/4})$ 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).

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