MIDAS: A Mixed Integer Dynamic Approximation Scheme

Andy Philpott 1 Faisal Wahid 1, 2 Frédéric Bonnans 2, 3
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
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 an ε-optimal policy when the Bellman functions are known to be continuous, and the sampling process satisfies standard assumptions.
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Andy Philpott, Faisal Wahid, Frédéric Bonnans. MIDAS: A Mixed Integer Dynamic Approximation Scheme. [Research Report] Inria Saclay Ile de France. 2016, pp.22. ⟨hal-01401950⟩

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