Condition that Richard Bellman derived for dynamic programming: “An optimal policy has the property that whatever the initial state and initial decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision.” (Bellman 1957, Chap. III.3)
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References
Bellman, R. E. (1957). Dynamic programming. Princeton, NJ: Princeton University Press.
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(2013). Principle of Optimality. In: Gass, S.I., Fu, M.C. (eds) Encyclopedia of Operations Research and Management Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1153-7_200636
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