# No-Regret Algorithms for Private Gaussian Process Bandit Optimization

arXiv: https://arxiv.org/abs/2102.12467 · HTML: https://mlsanity.com/paper/2102.12467/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 24 Feb 2021.

## Builds on (most cited first, 18 of 18)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Differentially Private Contextual Linear Bandits](https://mlsanity.com/paper/1810.00068/) (2018)
- [Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1706.00090/) (2017)
- [Random Fourier Features for Kernel Ridge Regression: Approximation Bounds and Statistical Guarantees](https://mlsanity.com/paper/1804.09893/) (2018)
- [RecoGym: A Reinforcement Learning Environment for the problem of Product Recommendation in Online Advertising](https://mlsanity.com/paper/1808.00720/) (2018)
- [Private Reinforcement Learning with PAC and Regret Guarantees](https://mlsanity.com/paper/2009.09052/) (2020)
- [Algorithms for Differentially Private Multi-Armed Bandits](https://mlsanity.com/paper/1511.08681/) (2015)
- [The Price of Differential Privacy For Online Learning](https://mlsanity.com/paper/1701.07953/) (2017)
- [Differential Privacy for Multi-armed Bandits: What Is It and What Is Its Cost?](https://mlsanity.com/paper/1905.12298/) (2019)
- [Quadrature-based features for kernel approximation](https://mlsanity.com/paper/1802.03832/) (2018)
- [Gaussian Quadrature for Kernel Features](https://mlsanity.com/paper/1709.02605/) (2017)
- [Bayesian Optimization for Policy Search via Online-Offline Experimentation](https://mlsanity.com/paper/1904.01049/) (2019)
- [GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation](https://mlsanity.com/paper/1401.2838/) (2014)
- [Local Differential Privacy: a tutorial](https://mlsanity.com/paper/1907.11908/) (2019)
- [Differentially Private Bayesian Optimization](https://mlsanity.com/paper/1501.04080/) (2015)
- [Personalized Gaussian Processes for Future Prediction of Alzheimer's Disease Progression](https://mlsanity.com/paper/1712.00181/) (2017)
- [Differentially Private Gaussian Processes](https://mlsanity.com/paper/1606.00720/) (2016)

## Built on by (most cited first, 11 of 11)

- [Shuffle Private Linear Contextual Bandits](https://mlsanity.com/paper/2202.05567/) (2022)
- [Differentially Private Regret Minimization in Episodic Markov Decision Processes](https://mlsanity.com/paper/2112.10599/) (2021)
- [Differentially Private Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2201.07052/) (2022)
- [On Differentially Private Federated Linear Contextual Bandits](https://mlsanity.com/paper/2302.13945/) (2023)
- [Differentially Private Episodic Reinforcement Learning with Heavy-tailed Rewards](https://mlsanity.com/paper/2306.01121/) (2023)
- [(Private) Kernelized Bandits with Distributed Biased Feedback](https://mlsanity.com/paper/2301.12061/) (2023)
- [Differentially Private Kernelized Contextual Bandits](https://mlsanity.com/paper/2501.07046/) (2025)
- [Concurrent Shuffle Differential Privacy Under Continual Observation](https://mlsanity.com/paper/2301.12535/) (2023)
- [Trigonometric Quadrature Fourier Features for Scalable Gaussian Process Regression](https://mlsanity.com/paper/2310.14544/) (2023)
- [DPMAC: Differentially Private Communication for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2308.09902/) (2023)
- [Differential Privacy in Kernelized Contextual Bandits via Random Projections](https://mlsanity.com/paper/2507.13639/) (2025)

## Abstract (arXiv)

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.