Projection-Free Bandit Optimization with Privacy Guarantees

TL;DR

This paper introduces the first differentially private algorithms for projection-free bandit convex optimization, achieving bounds comparable to non-private algorithms and extending privacy guarantees to complex decision sets without Euclidean projections.

Contribution

It presents the first private algorithms for projection-free bandit optimization, matching non-private bounds and broadening privacy in complex geometries.

Findings

Achieves $ ilde{O}(T^{3/4})$ regret bound matching non-private algorithms.

First to incorporate differential privacy into projection-free bandit optimization.

Extends privacy guarantees to decision sets with complex geometry like matroid polytopes.

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).