Achieving desired mechanical properties in additive manufacturing requires many experiments and a well-defined design framework becomes crucial in reducing trials and conserving resources. Here, we propose a methodology embracing the synergy between high-throughput (HT) experimentation and hierarchical machine learning (ML) to unveil the complex relationships between a large set of process parameters in Laser Powder Bed Fusion (LPBF) and selected mechanical properties (tensile strength and ductility). The HT method envisions the fabrication of small samples for rapid automated hardness and porosity characterization, and a smaller set of tensile specimens for more labor-intensive direct measurement of yield strength and ductility. The ML approach is based on a sequential application of Gaussian processes (GPs) where the correlations between process parameters and hardness/porosity are first learnt and subsequently adopted by the GPs that relate strength and ductility to process parameters. Finally, an optimization scheme is devised that leverages these GPs to identify the processing parameters that maximize combinations of strength and ductility. By founding the learning on larger easy-to-collect and smaller labor-intensive data, we reduce the reliance on expensive characterization and enable exploration of a large processing space. Our approach is material-agnostic and herein we demonstrate its application on 17-4PH stainless steel.