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jbrea / BayesianOptimization.jl

Bayesian optimization for Julia
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Return value of EI when variance is zero #22

Open ngiann opened 4 years ago

ngiann commented 4 years ago

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

jbrea commented 3 years ago

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.