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Is the philosophy between Bellman equations and minimax the same?

Both the algorithms look at the full horizon and take into account potential gains (Bellman) and potential losses (minimax).

However, do the two differ besides the obvious on the fact that Bellman equations use discounted potential rewards, while minimax deals with potential losses without the discount? Are these enough to say they are similar in philosophy or is are they dissimilar? If so, then in what sense?

Allright so the assumption of "two-players" sets them apart? – gfdsal – 2020-04-22T16:16:34.720

@gfdsal I guess so (at least in most cases), but minimax may also be used in other context and I don't exclude the existence of "Bellman equations" for two-player games (I am just not aware of them right now). – nbro – 2020-04-22T16:18:38.297