Solve a Dynamic Programming optimization problem using Neural Networks

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Good afternoon,
I have a dynamic programming problem (closed-loop, with three state variables), where each period's decision will directly impact other period's, and so they should be taken into account, with a series of constraints. Essentially, the goal is to define a rule within each period which can decide whether or not to perform action A, based on previous and future states, and a certain associated cost.
Is it possible to do the same problem using Neural Networks?

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