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This paper studies an accelerated fitted value iteration (FVI) algorithm tosolve high-dimensional Markov decision processes (MDPs). FVI is an approximatedynamic programming algorithm that has desirable theoretical properties.However, it can be intractable when the action space is finite butvector-valued. To solve such MDPs via FVI, we first approximate the valuefunctions by a two-layer neural network (NN) with rectified linear units (ReLU)being activation functions. We then verify that such approximators are strongenough for the MDP. To speed up the FVI, we recast the action selection problemas a two-stage stochastic programming problem, where the resulting recoursefunction comes from the two-layer NN. Then, the action selection problem issolved with a specialized multi-cut decomposition algorithm. More specifically,we design valid cuts by exploiting the structure of the approximated valuefunctions to update the actions. We prove that the decomposition can find theglobal optimal solution in a finite number of iterations and the overallaccelerated FVI is consistent. Finally, we verify the performance of the FVIalgorithm via a multi-facility capacity investment problem (MCIP). Acomprehensive numerical study is implemented, where the results show that theFVI is significantly accelerated without sacrificing too much in precision.

An Accelerated Fitted Value Iteration Algorithm for MDPs with Finite and Vector-Valued Action Space