To enhance the prediction accuracy of low-velocity impact performance and improve the structural design efficiency of triangular corrugated sandwich beams, this paper proposes a machine learning modeling and optimization process for the impact response of sandwich beams based on a hard-parameter-sharing multi-task learning (MTL) framework. A sample dataset is generated using finite element models, and the rationality of the models is validated against existing experimental results. Subsequently, an MTL model is trained to simultaneously predict the structural specific energy absorption (SEA), the maximum deflection of the top panel, and the initial peak load. The results show that the MTL model optimized via Bayesian optimization demonstrates strong predictive performance under a 50 J impact energy condition. The predictions align well with the finite element simulation results, with the coefficient of determination R² for all output variables in the test set exceeding 0.989, thereby validating the effectiveness and reliability of the model in response prediction and engineering optimization analysis. Parameter sensitivity analysis reveals that the core cell count and core wall thickness have the most significant influence on structural stiffness, followed by the top panel thickness, while the bottom panel thickness has a relatively minor impact. Moreover, the core wall thickness exhibits a certain saturation threshold in terms of performance enhancement. In combination with the non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ), multi-objective optimization analysis are conducted focusing on deformation characteristics, energy absorption performance, and comprehensive performance, and yields optimal parameter configurations that meet different engineering design requirements for sandwich beams.