We study the problem of approximating a model predictive controller (MPC) with learning models to facilitate real-time operation. In particular, we investigate how the use of a hybrid learning model can tighten the statistical learning bounds used for stability guarantees given by existing robust data-driven MPC approaches. We propose a hybrid learning framework with a finite set of state-dependent modes, each consisting of a supervised regression model. The mode-switching signal corresponds to a state space partition produced by solving a homotopy optimization problem that implicitly minimizes the Lipschitz constant of the regression model in each mode. The cardinality of the partition is decided by a bifurcation phenomenon, inducing a performance-complexity trade-off that is discussed. The proposed MPC approximation framework is validated on a nonlinear benchmark problem.