By John H. Holland
Strong, notwithstanding, the Amazon.com directory didn't say that this article was once geared for Ph.D.'s in arithmetic.
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Extra info for Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence
This extension does not add any generality to the framework (and henceis unnecessaryat the abstract level) becauseany randomnessinvolved , Adaptation in Natural and Artificial Systems in the interaction between the adaptive system and its environment can be subsumed in the stochastic action of the operators. (t . In particular , plans which receiveinformation in addition to payoff should do at least as well as plans which receiveonly payoff information . Thus, the efficiency of payoff-only plans with respectto 8 setsa nontrivial lower bound on the efficiency of other plans.
Briefly, their formulation is basedon a progressionoflortuneslo ,/ I ,/ 2' . . which the gambler attains a by sequenceof gambles. A gamble is naturally given as a probability distribution over the set of all possiblefortunes F. " The gambler' s rangeof choice for eachfortune I is dictated by the gamblinghouser . The strategy0' for confronting the houseis a function which at each time t selectsa gamble in r on the basisof the sequenceor partial history of fortunes to that time ( /0,/ 1, . . ,1,).
In more generalsituations, however, the plan will have to employ stochasticmixtures of pure strategiesand, if it is to exploit its opponents maximally, it will even associateparticular mixtures with particular kinds of opponents (assumingit is supplied with enough information to enable it to identify individual opponents). Considered in the (3, 8, x) framework, the strategies becomethe elements of the domain of action (t and the plans for employing thesestrategiesbecomeelements of 3. The set of admissibleenvironments8 dependsupon the particular case considered.
Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence by John H. Holland