In imperfect multiple-input multiple-output (MIMO) systems, model-based methods for performance prediction and optimization generally experience degradation in the dynamically changing environment with unknown interference and uncertain channel state information (CSI). To adapt to such challenging settings and better accomplish the network auto-tuning tasks, we propose a generic learnable model-driven framework. We further consider transmit regularized zero-forcing (RZF) precoding as a usage instance to illustrate the proposed framework. The overall process can be divided into three cascaded stages. First, we design a light neural network for refined prediction of sum rate based on coarse model-driven approximations. Then, the CSI uncertainty is estimated on the learned predictor in an iterative manner. In the last step the regularization term in the transmit RZF precoding is optimized. The effectiveness of the generic framework and the derivative method thereof is showcased via simulation results.