| 释义 |
▪ I. minimax, n. and a.|ˈmɪnɪmæks|
[f. minimum n. and a. + maximum.]
The smallest of a set of maxima; usu. attrib. (passing into adj.: see b), spec. designating (a) a strategy that minimizes the greatest loss or risk to which a participant in a game or other situation of conflict will be liable; (b) the theorem of game theory that states that, for a finite, zero-sum game with two players, the smallest maximum loss that a player can make himself liable to by a suitable choice of strategy is equal to the greatest minimum gain that he can guarantee himself. Cf. maximin n. and a.[1928J. von Neumann in Mathematische Annalen C. 307 (heading) Beweis des Satzes Max Min = Min Max. 1944― & Morgenstern Theory of Games xvii. 154 A slightly more general form of this Min-Max problem arises in another question of mathematical economics.] 1941Courant & Robbins What is Math.? vii. 345 (heading) Minimax points and topology. 1947A. Wald in Econometrica XV. 282 We shall refer to an admissible decision function η for which (1·6) takes its minimum value as a minimax solution of the problem. Ibid. 283 An element a0 in A is said to be a minimax strategy of player 1 if Infb K(a, b) takes its maximum value with respect to a for a = a0. 1949Ibid. XVII. 230 Often Nature's strategy is completely unknown. In that case Wald suggests that the statistician play a minimax strategy: that is, the statistician should select that decision procedure which minimizes the maximum risk. 1951Ann. Math. Statistics XXII. 466 The minimax risk is ½(1 - a). 1957Luce & Raiffa Games & Decisions i. 2 Although Borel gave a clear statement of an important class of game theoretic problems and introduced the concepts of pure and mixed strategies, von Neumann points out that he did not obtain one crucial result—the minimax theorem—without which no theory of games can be said to exist. 1958Engineering 21 Mar. 369/2 Player B, on the other hand, will determine the largest value in each column, and the smallest of these, the ‘minimax’. 1961L. Weiss Statistical Decision Theory v. 89 The minimax criterion has been criticized as being too conservative. 1962Sci. Amer. Dec. 114/2 Both firms were guided by the principle of the minimax, choosing the best of the worst outcomes. 1968Brit. Med. Bull. XXIV. 232/2 This would be the Bayesian Strategy of decision theory.., but other strategies, such as minimax or restricted Bayes, could also be used. 1970[see maximin n. and a.]. 1972Computer Jrnl. XV. 277 (heading) On minimax solutions of linear equations.
b. Used predicatively as adj.: equal to, or resulting in, a minimax value.
1952Ann. Math. Statistics XXIII. 587 For such weight functions the supremum of the risk over all θ ε Ω is infinite for every decision function, so that every decision function is minimax. 1965Wozencraft & Jacobs Princ. Communication Engin. ii. 118 The decision rule which has the smallest maximum probability of error is called the minimax decision rule. Which of the eight rules is minimax? 1970R. B. Ash Basic Probability Theory viii. 250 Find a minimax test, that is, a test that minimizes max (α, β). It is immediate from the definition of admissibility that an admissible test with constant risk (i.e., α = β) is minimax.
▪ II. minimax, v.|ˈmɪnɪmæks|
[f. prec. n.]
a. trans. To make equal to a minimax value.
b. intr. To adopt or employ a minimax strategy. So ˈminimaxing vbl. n. and ppl. a.
1964Gould & Kolb Dict. Social Sci. 573/2 The goal may be assumed to take the form of maximizing (or, in game theory, minimaxing) the expected value, over some time interval, of a utility function. 1968Listener 4 Apr. 438/1 Just like that 50–50 combination of heads and tails, the minimaxing peasant might pick a 40–60 combination of wheat and millet. 1973Nature 23 Feb. 507/1 The fundamental mechanism underlying all this work [on machines designed to play games] has been a cycle of processes: lookahead, evaluation and minimaxing. |