Algorithm 2 Adaptive GP Random Sampling Algorithm

$$\begin{array}{cc}\hfill & \mathbf{Input}:{\mathit{X}}_0,{\mathit{y}}_0,n_0,n_{\mathcal{A}},{\widehat{p}}_{n_0}(\mathit{x})\hfill \\ \hfill & \mathrm{Output}:\mathit{X},\mathit{y}\hfill \\ \hfill & 1\mathit{X}={\mathit{X}}_0;\hfill \\ \hfill & 2\mathbf{for}\ell =n_0\dots ,N\mathbf{do}\hfill \\ \hfill & 3\mid \begin{array}{c}\text{Sample}{\mathit{x}}_{\ell }\text{from}{\widehat{p}}_{\ell }(\mathit{x});\hfill \\ \text{Get MEP}{y}_{\ell }\text{at loci}{\mathit{x}}_{\ell };\hfill \\ \text{Make}\mathit{X}=[{\mathit{X}}^{\mathsf{T}},{\mathit{x}}_{\ell }^{\mathsf{T}}{]}^{\mathsf{T}}\text{and}\mathit{y}=[{\mathit{y}}^{\mathsf{T}},y_{\ell }{]}^{\mathsf{T}};\hfill \\ \text{Update}{\widehat{p}}_{\ell }(\mathit{x})\text{using the pair}\{\mathit{X},\mathit{y}\};\hfill \end{array}\phantom{\mid }\hfill \\ \hfill & 7\mathbf{end}\hfill \\ \hfill & 8\mathbf{return}\mathit{X},\mathit{y};\hfill \end{array}$$