  Angle-resolved photoemission spectroscopy (ARPES) is a technique used to map
the occupied electronic structure of solids. Recent progress in X-ray focusing
optics has led to the development of ARPES into a microscopic tool, permitting
the electronic structure to be spatially mapped across the surface of a sample.
This comes at the expense of a time-consuming scanning process to cover not
only a three-dimensional energy-momentum ($E, k_z, k_y$) space but also the
two-dimensional surface area. Here, we implement a protocol to autonomously
search both $\mathbf{k}$- and real space in order to find positions of
particular interest, either because of their high photoemission intensity or
because of sharp spectral features. The search is based on the use of Gaussian
process regression and can easily be expanded to include additional parameters
or optimisation criteria. This autonomous experimental control is implemented
on the SGM4 micro-focus beamline of the synchrotron radiation source ASTRID2.
