On the Sublinear Regret of GP-UCB

Authors: Justin Whitehouse, Aaditya Ramdas, Steven Z. Wu

NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical In this work, we resolve this open question and show that GP-UCB enjoys nearly optimal regret. In particular, our results yield sublinear regret rates for the Mat ern kernel, improving over the state-of-the-art analyses and partially resolving a COLT open problem posed by Vakili et al. Our improvements rely on a key technical contribution regularizing kernel ridge estimators in proportion to the smoothness of the underlying kernel k. Applying this key idea together with a largely overlooked concentration result in separable Hilbert spaces (for which we provide an independent, simplified derivation), we are able to provide a tighter analysis of the GP-UCB algorithm.
Researcher Affiliation Academia Justin Whitehouse Carnegie Mellon University jwhiteho@andrew.cmu.edu Zhiwei Steven Wu Carnegie Mellon University zstevenwu@cmu.edu Aaditya Ramdas Carnegie Mellon University aramdas@cmu.edu
Pseudocode Yes Algorithm 1 Gaussian Process Upper Confidence Bound (GP-UCB)
Open Source Code No The paper does not provide any links to open-source code or state that the source code for the described methodology is available.
Open Datasets No The paper is theoretical and does not conduct experiments on datasets, thus it does not provide information about public dataset availability for training.
Dataset Splits No The paper is theoretical and does not conduct empirical studies involving dataset splits for training, validation, or testing.
Hardware Specification No The paper is theoretical and does not describe any experimental setup requiring specific hardware specifications.
Software Dependencies No The paper is theoretical and does not discuss specific software dependencies with version numbers for experimental reproducibility.
Experiment Setup No The paper is theoretical and does not describe an experimental setup with hyperparameter values or training configurations.