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from Brown Corpus
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The essential characteristic of an optimal policy when the state of the stream is transformed in a sequence of stages with no feedback was first isolated by Bellman.
He recognized that whatever transformation may be effected in the first stage of an R-stage process, the remaining stages must use an optimal Af-stage policy with respect to the state resulting from the first stage, if there is to be any chance of optimizing the complete process.
Moreover, by systematically varying the operating conditions in the first stage and always using the optimal Af-stage policy for the remaining stages, we shall eventually find the optimal policy for all R stages.
Proceeding in this way, from one to two and from two to three stages, we may gradually build up the policy for any number.
At each step of the calculation the operating variables of only one stage need be varied.

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