To exploit the full industrial potential of additive manufacturing (AM) beyond prototyping, the resource-consuming identification of the optimal processing conditions needs to be minimized. Machine learning (ML) approaches are ideal for realizing this task. We employ multi-objective optimization using Gaussian Process Regression to model and predict target properties and their uncertainties of parts fabricated by laser powder bed fusion (LPBF) — a widely used metal AM technology. With density and amorphicity as target parameters, we optimize models using the Pareto front facilitated by the Non-Dominated Sorting Genetic Algorithm II. Despite deviations in the amorphicity data, we demonstrate this method to identify the high-performance region of the process parameters and its ability to be iteratively enhanced with additional experimental data. This bi-objective optimization approach provides a robust toolset for navigating LPBF processing. It can be easily extended to a larger set of target properties and transferred to further AM technologies.