Noisy Expected Improvement under a Gaussian process prior converges at rate O(t^{-1/2} log^{(d+1)/2} t) for squared exponential kernels and O(t^{-nu/(2nu+d)} log^{nu/(2nu+d)} t) for Matérn kernels.
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On the convergence rate of noisy Bayesian Optimization with Expected Improvement
Noisy Expected Improvement under a Gaussian process prior converges at rate O(t^{-1/2} log^{(d+1)/2} t) for squared exponential kernels and O(t^{-nu/(2nu+d)} log^{nu/(2nu+d)} t) for Matérn kernels.