Material classification is a fundamental problem in computer vision and plays a crucial role in scene understanding. Previous studies have explored various material recognition methods based on reflection properties such as color, texture, specularity, and scattering. Among these cues, polarization is particularly valuable because it provides rich material information and enables recognition even at distances where capturing high-resolution texture is impractical. However, measuring polarimetric reflectance properties typically requires multiple modulations of the polarization state of the incident light, making the process time-consuming and often unnecessary for certain recognition tasks. While material classification can be achieved using only a subset of polarimetric measurements, the optimal configuration of measurement angles remains unclear. In this study, we propose an end-to-end optimization framework that jointly learns a material classifier and determines the optimal combinations of rotation angles for polarization elements that control both the incident and reflected light states. Using our Mueller-matrix material dataset, we demonstrate that our method achieves high-accuracy material classification even with a limited number of measurements.