MIDAS: A Mixed Integer Dynamic Approximation Scheme.

Summary Mixed Integer Dynamic Approximation Scheme (MIDAS) is a new sampling-based algorithm for solving finite-horizon stochastic dynamic programs with monotonic Bellman functions. MIDAS approximates these value functions using step functions, leading to stage problems that are mixed integer programs. We provide a general description of MIDAS, and prove its almost-sure convergence to an ε-optimal policy when the Bellman functions are known to be continuous, and the sampling process satisfies standard assumptions.