🤖 AI Summary
To address the high computational cost and curse of dimensionality in high-dimensional Bayesian optimization, this paper proposes the Expected Coordinate Improvement (ECI) acquisition function—the first to incorporate coordinate descent into acquisition design: at each iteration, ECI greedily optimizes along a single coordinate axis, circumventing full-space search. We prove ECI’s consistency theoretically. Practically, ECI integrates a Gaussian process surrogate, coordinate-aligned gradient approximation, randomized coordinate selection, and Monte Carlo estimation for efficient evaluation. On 100-dimensional benchmark functions, ECI achieves an 8.2× speedup over Expected Improvement (EI) and GP-UCB, while improving simple regret convergence by 37%. Its efficacy and practicality are further validated on neural network hyperparameter tuning tasks.