Free-Electron Lasers like the one at the SLAC National Accelerator Laboratory are sources of extremely bright X-rays that are useful in a variety of scientific imaging applications. Because there are only a handful of FEL facilities around the world, access to these X-rays is in high demand. Every year, hundreds of hours are spent tuning quadrupole focusing magnets to optimize the X-ray brightness. During this tuning process, the beam typically cannot be used for experiments. In this thesis, I show that by performing Bayesian optimization using a Gaussian process regression model containing prior information derived from an optical model of the accelerator in combination with historical data, we were able to significantly reduce the amount of time spent tuning the quadrupoles in comparison to previous methods.