# Time-Varying Gaussian Process Bandits with Unknown Prior

arXiv: https://arxiv.org/abs/2402.01632 · HTML: https://mlsanity.com/paper/2402.01632/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 30 references that are in the map.
- First posted on arXiv 2 Feb 2024.

## Builds on (most cited first, 11 of 11)

- [Corralling a Band of Bandit Algorithms](https://mlsanity.com/paper/1612.06246/) (2016)
- [Provably Efficient Online Hyperparameter Optimization with Population-Based Bandits](https://mlsanity.com/paper/2002.02518/) (2020)
- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [Time-Varying Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1601.06650/) (2016)
- [Regret Bound Balancing and Elimination for Model Selection in Bandits and RL](https://mlsanity.com/paper/2012.13045/) (2020)
- [Weighted Gaussian Process Bandits for Non-stationary Environments](https://mlsanity.com/paper/2107.02371/) (2021)
- [Self-Correcting Bayesian Optimization through Bayesian Active Learning](https://mlsanity.com/paper/2304.11005/) (2023)
- [Regret Balancing for Bandit and RL Model Selection](https://mlsanity.com/paper/2006.05491/) (2020)
- [No-Regret Algorithms for Time-Varying Bayesian Optimization](https://mlsanity.com/paper/2102.06296/) (2021)
- [On Controller Tuning with Time-Varying Bayesian Optimization](https://mlsanity.com/paper/2207.11120/) (2022)
- [Bayesian Optimization for Dynamic Problems](https://mlsanity.com/paper/1803.03432/) (2018)

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

- [Statistical Multicriteria Evaluation of LLM-Generated Text](https://mlsanity.com/paper/2506.18082/) (2025)
- [Alignment Quality Index (AQI) : Beyond Refusals: AQI as an Intrinsic Alignment Diagnostic via Latent Geometry, Cluster Divergence, and Layer wise Pooled Representations](https://mlsanity.com/paper/2506.13901/) (2025)
- [Bayesian Optimisation with Unknown Hyperparameters: Regret Bounds Logarithmically Closer to Optimal](https://mlsanity.com/paper/2410.10384/) (2024)
- [A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Lifting](https://mlsanity.com/paper/2404.12219/) (2024)
- [Adaptive Prior Selection in Gaussian Process Bandits with Thompson Sampling](https://mlsanity.com/paper/2502.01226/) (2025)
- [Just One Layer Norm Guarantees Stable Extrapolation](https://mlsanity.com/paper/2505.14512/) (2025)
- [Regret Analysis of Guided Diffusion for Black-Box Optimization over Structured Inputs](https://mlsanity.com/paper/2605.10385/) (2026)
- [Weighted Wasserstein Barycenter of Gaussian Processes for exotic Bayesian Optimization tasks](https://mlsanity.com/paper/2602.09181/) (2026)
- [Sharper Regret Bounds for Time-Varying Gaussian Process Bandits with Constant Exploration](https://mlsanity.com/paper/2608.18863/) (2026)
- [Online Adaptive Kernel Mixing for Gaussian Process Decision Making](https://mlsanity.com/paper/2609.19891/) (2026)
- [Bayesian Optimization of CVaR with Unknown Hyperparameters](https://mlsanity.com/paper/2610.18306/) (2026)

## Abstract (arXiv)

Bayesian optimisation requires fitting a Gaussian process model, which in turn requires specifying prior on the unknown black-box function -- most of the theoretical literature assumes this prior is known. However, it is common to have more than one possible prior for a given black-box function, for example suggested by domain experts with differing opinions. In some cases, the type-II maximum likelihood estimator for selecting prior enjoys the consistency guarantee, but it does not universally apply to all types of priors. If the problem is stationary, one could rely on the Regret Balancing scheme to conduct the optimisation, but in the case of time-varying problems, such a scheme cannot be used. To address this gap in existing research, we propose a novel algorithm, PE-GP-UCB, which is capable of solving time-varying Bayesian optimisation problems even without the exact knowledge of the function's prior. The algorithm relies on the fact that either the observed function values are consistent with some of the priors, in which case it is easy to reject the wrong priors, or the observations are consistent with all candidate priors, in which case it does not matter which prior our model relies on. We provide a regret bound on the proposed algorithm. Finally, we empirically evaluate our algorithm on toy and real-world time-varying problems and show that it outperforms the maximum likelihood estimator, fully Bayesian treatment of unknown prior and Regret Balancing.