In this study, a thin film of Si-Ge-Sn alloy with a gradient composition distribution was synthesized using combinatorial magnetron sputtering. This thin-film ternary material library was electrochemically characterized as a lithium-ion anode on a millimeter-scale using a three-electrode half-cell scanning droplet cell. The experimental protocol was driven by automated on-the-fly electrochemical analysis and Bayesian optimization with a Gaussian process to find the chemical composition with the highest specific capacity. Comparative analysis revealed a significant improvement in Li-ion battery performance with the best-performing Si-Ge-Sn anodes outperforming those with conventional graphite anodes, with increases in gravimetric energy densities of over 30%. Advanced high-throughput µ-XRF and Raman spectroscopy provided valuable insights into the composition-structure-property relationships of the Si-Ge-Sn system. Additionally, the results of XPS and EIS studies were used to elucidate the discrepancies between theoretical and experimental reversible capacities of Si- and Ge-rich compounds.