If you formulate the problem as a Markov decision process, you can use 
POMDPs.jl <https://github.com/sisl/POMDPs.jl> which supports value iteration 
<https://github.com/sisl/DiscreteValueIteration.jl>. The POMDPs.jl 
framework requires a functional problem definition, and some examples can 
be found in POMDPModels.jl <https://github.com/sisl/POMDPModels.jl>. 

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