# Bayesian Analysis of Combinatorial Gaussian Process Bandits

arXiv: https://arxiv.org/abs/2312.12676 · HTML: https://mlsanity.com/paper/2312.12676/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 46 references that are in the map.
- First posted on arXiv 20 Dec 2023.

## Builds on (most cited first, 13 of 13)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Taming the Monster: A Fast and Simple Algorithm for Contextual Bandits](https://mlsanity.com/paper/1402.0555/) (2014)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Natural Gradients in Practice: Non-Conjugate Variational Inference in Gaussian Process Models](https://mlsanity.com/paper/1803.09151/) (2018)
- [Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds](https://mlsanity.com/paper/2302.01511/) (2023)
- [Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian Regret Bounds](https://mlsanity.com/paper/2311.03760/) (2023)
- [Online Learning of Energy Consumption for Navigation of Electric Vehicles](https://mlsanity.com/paper/2111.02314/) (2021)
- [Optimal Epidemic Control as a Contextual Combinatorial Bandit with Budget](https://mlsanity.com/paper/2106.15808/) (2021)
- [Contextual Combinatorial Bandits with Changing Action Sets via Gaussian Processes](https://mlsanity.com/paper/2110.02248/) (2021)
- [Contextual Combinatorial Multi-output GP Bandits with Group Constraints](https://mlsanity.com/paper/2111.14778/) (2021)

## Built on by (most cited first, 2 of 2)

- [Adaptive Prior Selection in Gaussian Process Bandits with Thompson Sampling](https://mlsanity.com/paper/2502.01226/) (2025)
- [Learning to Attack: A Bandit Approach to Adversarial Context Poisoning](https://mlsanity.com/paper/2603.00567/) (2026)

## Abstract (arXiv)

We consider the combinatorial volatile Gaussian process (GP) semi-bandit problem. Each round, an agent is provided a set of available base arms and must select a subset of them to maximize the long-term cumulative reward. We study the Bayesian setting and provide novel Bayesian cumulative regret bounds for three GP-based algorithms: GP-UCB, GP-BayesUCB and GP-TS. Our bounds extend previous results for GP-UCB and GP-TS to the infinite, volatile and combinatorial setting, and to the best of our knowledge, we provide the first regret bound for GP-BayesUCB. Volatile arms encompass other widely considered bandit problems such as contextual bandits. Furthermore, we employ our framework to address the challenging real-world problem of online energy-efficient navigation, where we demonstrate its effectiveness compared to the alternatives.