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Randomized algorithms as zero-sum games : ウィキペディア英語版 | Randomized algorithms as zero-sum games
Randomized algorithms are algorithms that employ a degree of randomness as part of their logic. These algorithms can be used to give good average-case results (complexity-wise) to problems which are hard to solve deterministically, or display poor worst-case complexity. An algorithmic game theoretic approach can help explain why in the average case randomized algorithms may work better than deterministic algorithms. ==Formalizing the game== Consider a zero-sum game between player A, whose strategies are deterministic algorithms, and player B, who’s strategies are inputs for A’s algorithms. The cost of a strategy profile is the running time of A’s chosen algorithm on B’s chosen input. Therefore, player A tries to minimize the cost, and player B tries to maximize it. In the world of pure strategies, for every algorithm that A chooses, B may choose the most costly input – this is the worst-case scenario, and can be found using standard complexity analysis. But in the real world, inputs are normally not selected by an ‘evil opponent’ – rather, they come from some distribution over inputs. Since this is the case, if we allow the algorithms to also be drawn from some distribution, we may look at the game as one that allows mixed strategies. That is, each player chooses a distribution over its strategies.
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Randomized algorithms as zero-sum games」の詳細全文を読む
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