Regret Bounds for Expected Improvement Algorithms in Gaussian Process Bandit Optimization

@article{TranThe2022RegretBF,
  title={Regret Bounds for Expected Improvement Algorithms in Gaussian Process Bandit Optimization},
  author={Hung Tran-The and S. Gupta and Santu Rana and Svetha Venkatesh},
  journal={ArXiv},
  year={2022},
  volume={abs/2203.07875}
}
The expected improvement (EI) algorithm is one of the most popular strategies for optimization under uncertainty due to its simplicity and efficiency. Despite its popularity, the theoretical aspects of this algorithm have not been properly analyzed. In particular, whether in the noisy setting, the EI strategy with a standard incumbent converges is still an open question of the Gaussian process bandit optimization problem. We aim to answer this question by proposing a variant of EI with a standard… 

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