Matrix multiplication is a fundamental building block for modern information processing and artificial intelligence algorithms. Photonics-based matrix multipliers have recently attracted much attention due to their advantages of low energy and ultrafast speed. Conventionally, achieving matrix multiplication relies on bulky Fourier optical components, and the functionalities are unchangeable once the design is determined. Furthermore, the bottom-up design strategy cannot easily be generalized into concrete and practical guidelines. Here, we introduce a reconfigurable matrix multiplier driven by on-site reinforcement learning. The constituent transmissive metasurfaces incorporating varactor diodes serve as tunable dielectrics based on the effective medium theory. We validate the viability of tunable dielectrics and demonstrate the performance of matrix customization. This work represents a new avenue in realizing reconfigurable photonic matrix multipliers for on-site applications.