Reactive multi-principal element alloys （RMPEAs）， combining superior mechanical properties with high heat of oxidation， possess significant application potential in the field of energetic structural materials. Currently， research on the mechanical properties of these materials focuses predominantly on quasi-static compression. Data regarding tensile yield strength， which governs the structural load-bearing limit and impact-induced fragmentation and energy release characteristics， remain relatively scarce. Furthermore， due to the limited dataset size and strong non-linearity， traditional trial-and-error methods struggle to achieve precise prediction and targeted design of tensile yield strength within the vast compositional space. This study proposes a machine learning-driven design strategy to address the challenges of predicting and optimizing the tensile yield strength of RMPEAs under small-sample conditions. Based on a collected dataset of 88 as-cast RMPEAs and incorporating 33 domain-knowledge-integrated physical descriptors， prediction models were constructed using five machine learning algorithms， with a genetic algorithm employed for feature dimensionality reduction. The results demonstrate that the optimal Support Vector Regression （SVR） model achieves a coefficient of determination （R²） of 0.928 on the test set. SHapley Additive explanation （SHAP） interpretability analysis reveals that the difference in melting points of the constituent elements is the most critical factor influencing yield strength， while differences in atomic radius and electronegativity also play significant positive roles. Inverse design of the compositional space based on the model predicts that within the Ti-Zr-Nb-Ta system， increasing Ta content while reducing Nb content can significantly enhance tensile yield strength. The experimentally fabricated TiZrNbTa_x series alloys validated this trend， confirming the effectiveness and accuracy of this data-driven paradigm for the design of high-performance reactive multi-principal element energetic structural materials.