State-of-the-art schemes for performance analysis and optimization of multiple-input multiple-output systems generally experience degradation or even become invalid in dynamic complex scenarios with unknown interference and channel state information (CSI) uncertainty. To adapt to the challenging settings and better accomplish these network auto-tuning tasks, we propose a generic learnable model-driven framework in this paper. To explain how the proposed framework works, we consider regularized zero-forcing precoding as a usage instance and design a light-weight neural network for refined prediction of sum rate and detection error based on coarse model-driven approximations. Then, we estimate the CSI uncertainty on the learned predictor in an iterative manner and, on this basis, optimize the transmit regularization term and subsequent receive power scaling factors. A deep unfolded projected gradient descent based algorithm is proposed for power scaling, which achieves favorable trade-off between convergence rate and robustness.