No-Regret Algorithms for Private Gaussian Process Bandit Optimization
This addresses privacy concerns in data-driven optimization for applications like healthcare or finance, though it builds incrementally on existing GP bandit methods.
The paper tackles the problem of Gaussian process bandit optimization with privacy constraints, proposing differentially private algorithms that combine kernel approximation with random perturbations. The result is provably no-regret algorithms for joint and local differential privacy settings that are computationally efficient for stationary kernels.
The widespread proliferation of data-driven decision-making has ushered in a recent interest in the design of privacy-preserving algorithms. In this paper, we consider the ubiquitous problem of gaussian process (GP) bandit optimization from the lens of privacy-preserving statistics. We propose a solution for differentially private GP bandit optimization that combines a uniform kernel approximator with random perturbations, providing a generic framework to create differentially-private (DP) Gaussian process bandit algorithms. For two specific DP settings - joint and local differential privacy, we provide algorithms based on efficient quadrature Fourier feature approximators, that are computationally efficient and provably no-regret for popular stationary kernel functions. Our algorithms maintain differential privacy throughout the optimization procedure and critically do not rely explicitly on the sample path for prediction, making the parameters straightforward to release as well.