Precise control of the electron beam probe is critical in scanning transmission electron microscopy (STEM) to understanding materials at atomic level. However, the nature of magnetic lenses introduces various orders of aberrations and make aberration corrector tuning a complex and time costly procedure. In this paper, we show that a deep neural network can accurately capture phase space variations from electron Ronchigrams, diffraction patterns from amorphous materials, allowing for the mapping to a single beam quality metric. A Bayesian approach is adopted to optimize the aberration correctors while providing the full posterior of the response to account for uncertainties. Furthermore, a deep kernel is implemented and shown to improve performance by effectively learning the correlations between input dimensions. This new scheme targets fully automated aberration corrector tuning, achieving greater speed and less human bias.