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Return value of EI when variance is zero

Open ngiann opened this issue 5 years ago • 1 comments

Similarly to a previous issue #21

https://github.com/jbrea/BayesianOptimization.jl/blob/5ce078b50c1447860e5465eae0fe0be0600b671a/src/acquisitionfunctions.jl#L48

I noticed that given that the variance is 0 you may return `μ - a.τ`` if this difference is positive and otherwise 0. However, I see that equation (4) in "A Tutorial on Bayesian Optimization of..." the return value of EI is always zero if the variance is zero.

Cheers

ngiann avatar Oct 09 '20 08:10 ngiann

The limit of EI for σ² to 0 is μ > a.τ ? μ - a.τ : 0., because the second term vanishes and the cdf in the first term approaches 1 when μ > a.τ and 0 otherwise. I think the comment "... and vanishes otherwise" in the tutorial is misleading.

jbrea avatar Feb 11 '21 19:02 jbrea