ppgaluzio
commented
1 year ago Thank you @yufeng0929 !
Yes, the code doesn't have the acquisition function clearly implemented, but it is possible to write the method in such terms. Here is how you would write the acquisition function in this case:
The method described in the manuscript can be interpreted as the maximization of an acquisition function $A (\vec x)$, given by:
$$ A(\vec x; t) = q \left( \frac{d{f}(\vec x; t) - \mu{f}(t)}{\sigma{f}(t)} \right) + (1-q) \left( \frac{d{x}(\vec x; t)-\mu{x}(t)}{\sigma{x}(t)} \right) \qquad \forall\; \vec x \in \chi_{t} $$
where $\chi_{t}$ is the Pareto Set of $\vec \eta(\vec x; t)$, and:
$$ \begin{aligned} d{f}(\vec x; t) &= \min{\tau\in{0,\ldots,t}}\left(\left|\vec f(\vec x)-\vec f(\vec x\,^{(\tau)})\right|\right) \ \mu{f}(t) &= \int{\chi{t}}d{f}(\vec x; t)p(\vec x)\,d\vec x \ \sigma{f}(t) &= \sqrt{\int{\chi{t}}(d{f}(\vec x; t) - \mu{f}(t))^{2}p(\vec x)\,d\vec x} \ d{x}(\vec x; t) &= \min_{\tau\in{0,\ldots,t}}\left(\left|\vec x-\vec x\,^{(\tau)}\right|\right) \end{aligned} $$
where $p(\vec x)$ is the density of $\vec x$ on $\chi{t}$, and the definitions to $\mu{x}(t)$ and $\sigma{x}(t)$ are analogous to those of $\mu{f}(t)$ and of $\sigma_{f}(t)$, respectively.
yufeng0929
Hello @ppgaluzio, I love your code of MOBOpt. It's very useful and help me a lot! But I also have a question. I know many MOBO models use 'acquision function' to select next point when iterating. However, I read your code and didn't find your 'acquision functions'. If your code has this, could you tell me where is it? If your code dosen't have 'acquision function', could you tell me what you use to replace 'acquision function' and its theory? Thanks for your help!