Abstract
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 a $$2T\varepsilon $$-optimal policy for problems with T stages when the Bellman functions are known to be monotonic, and the sampling process satisfies standard assumptions.
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