Table 2 Bayesian algorithm.
1. | \(Input:initial\;data~\;\varvec{Di},\varvec{~}\# \varvec{Iteration}\) |
2. | \(\begin{gathered} {\text{chose}}\;x_{t} \;by\;optimizing\;the\;acquisition\;function,~\;a_{t} \;over\;the\;GP~ \hfill \\ such\;that:~\varvec{x}_{\varvec{t}} = \varvec{arg}\;\varvec{~}\mathop \mathbf{\max }\limits_{\varvec{x}} \varvec{a}\left( {\varvec{xID}} \right) \hfill \\ \end{gathered}\) |
3. | \(sample\;the\;objective\;function:~\varvec{y}_{\varvec{t}} = \varvec{f}\left( {\varvec{x}_{\varvec{t}} } \right) + \in _{\varvec{t}}\) |
4. | \(Augument\;the\;data:~\varvec{D}_{\varvec{t}} = \left\{ {\varvec{D}_{{1:\varvec{t} - 1}} \cup \left( {\varvec{x}_{\varvec{t}} ,varvec{~~y}_{\varvec{t}} } \right)\} } \right.\) |
5. | Repeat 1 until the maximum number of iterations is reached. |