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Equation 5 · Part 4 · AI for Science and Medicine in Practice: An Advanced Technical Guide

Symbol f^+

EI(x)=E ⁣[max⁡(f(x)−f+, 0)],\mathrm{EI}(x) = \mathbb{E}\!\left[\max(f(x) - f^{+},\ 0)\right],
f+f^{+}

What this part means

the current best observed value.

Its job in the formula

f+f^+ appears in the objective or constraint used by the optimization on the right.

Where the article explains it

The standard fix is an acquisition function such as expected improvement, which for a candidate x with predictive mean μ(x)\mu(x) , predictive standard deviation σ(x)\sigma(x) , and current best observed value f+f^{+} is EI(x)=E ⁣[max⁡(f(x)−f+, 0)]\mathrm{EI}(x) = \mathbb{E}\!\left[\max(f(x) - f^{+},\ 0)\right].

The passage around this formula

…already believe. The standard fix is an acquisition function such as expected improvement, which for a candidate x with predictive mean μ(x)\mu(x) , predictive standard deviation σ(x)\sigma(x) , and current best observed value f+f^{+} is EI(x)=E ⁣[max⁡(f(x)−f+, 0)]\mathrm{EI}(x) = \mathbb{E}\!\left[\max(f(x) - f^{+},\ 0)\right]. a quantity that rewards both a high predicted mean and high predictive uncertainty. In practice this means the loop deliberately spends some experimental budget on candidates the model is unsure about, not only on candidates it is confident are good — because the…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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