ProjectionFree Bandit Optimization with Privacy Guarantees
Abstract
We design differentially private algorithms for the bandit convex optimization problem in the projectionfree 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 differentiallyprivate algorithm for projectionfree bandit optimization, and in fact our bound of $\widetilde{O}(T^{3/4})$ matches the best known nonprivate projectionfree algorithm (GarberKretzu, AISTATS `20) and the best known private algorithm, even for the weaker setting when projections are available (SmithThakurta, NeurIPS `13).
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 arXiv:
 arXiv:2012.12138
 Bibcode:
 2020arXiv201212138E
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Cryptography and Security;
 Computer Science  Data Structures and Algorithms;
 Mathematics  Optimization and Control
 EPrint:
 Appears in AAAI21