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. This task becomes more challenging when multiple properties of the part shall be simultaneously optimized. We utilize machine learning (ML) methods in a case study on laser powder bed fusion (LPBF) of a Zr-based glass-forming alloy. Our experiments show that processing parameters affect density and amorphicity opposingly, demonstrating the efficacy of our ML-based approach. We employ multi-objective optimization using Gaussian Process Regression to model and predict target properties and their uncertainties of parts fabricated by 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.