We propose a generic method for solving infinite-horizon, discrete-time dynamic incentive problems with hidden states. We first combine set-valued dynamic programming techniques with Bayesian Gaussian mixture models to determine irregularly shaped equilibrium value correspondences. Second, we generate training data from those pre-computed feasible sets to recursively solve the dynamic incentive problem by a massively parallelized Gaussian process machine learning algorithm. This combination enables us to analyze
models of a complexity that was previously considered to be intractable. To demonstrate the broad applicability of our framework, we compute solutions for models of repeated agency with history dependence, many types, and varying preferences.