Machine learning for dynamic incentive problems

We present a flexible and scalable computational framework integrating machine learning and optimization theory to solve dynamic adverse selection models with persistent private information and many types. Our approach reformulates the model into a numerically tractable structure that bypasses set-valued dynamic programming; we formally prove that, under verifiable conditions, this relaxation yields the solution to the original problem. The recast problem is solved via a parallelized value function iteration algorithm, where high-dimensional, nonlinear functions are approximated using Gaussian process regression combined with Bayesian active learning. We apply our framework to two previously intractable models: one with persistent hidden information involving up to ten types and another incorporating multiple persistent types and overreporting. Validation against known solutions and rigorous credibility measures confirms accuracy. Allowing overreporting significantly alters long-run contract outcomes, concentrating consumption away from extremes and smoothing utility promises over time.