Theoretical Understanding of Gaussian Process Bandits in Practical Applications

Licentiate thesis, 2026

Bayesian optimization (BO) provides a principled framework for optimizing blackbox functions with noisy outputs, with applications ranging from aircraft design to hyperparameter tuning. BO algorithms can be theoretically analyzed through the lens of Gaussian process (GP) bandits, providing theoretical guarantees of their efficiency. This thesis provides theoretical analyses and experimental evaluation of GP bandit algorithms with relevance to practical applications.

The first part of the thesis is motivated by the need for navigation systems that prioritize energy-efficiency and adapt to collected data. As such, we develop a combinatorial GP bandit framework for online energy-efficient navigation of electric vehicles. We theoretically analyze three algorithms under this framework, providing bounds on their regret. The algorithms are evaluated on real-world road networks, demonstrating that they explore the road network more efficiently compared to previous work.

The second part of the thesis is focused on addressing a discrepancy between theory and practice. The theoretical literature commonly assumes that important characteristics (the prior) of the blackbox function being optimized is known before the optimization process starts. However in practice, the prior must often be inferred from the data, which invalidates any theoretical guarantees. To address this issue, we theoretically analyze two algorithms that simultaneously learn the prior and optimize the unknown function. We identify issues in previous theoretical analyses, correct and improve upon their results. Finally, we experimentally evaluate the algorithms on synthetic and real-world data and demonstrate their effectiveness at simultaneous optimization and prior identification.