Projection-Free Bandit Optimization with Privacy Guarantees
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).
- Publication:
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arXiv e-prints
- Pub Date:
- December 2020
- DOI:
- 10.48550/arXiv.2012.12138
- arXiv:
- arXiv:2012.12138
- Bibcode:
- 2020arXiv201212138E
- Keywords:
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- Computer Science - Machine Learning;
- Computer Science - Cryptography and Security;
- Computer Science - Data Structures and Algorithms;
- Mathematics - Optimization and Control
- E-Print:
- Appears in AAAI-21