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optimality" would be that for all utility functions of interest the ratio of the rate of accrual of the adaptive plan t, Ut(T)/T, to that of Cb*(E), Ub*(E)(T)/T, approaches 1 for each  . That is, |
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Generally there will be some additional requirement that the rates be comparable for all times T. |
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Adaptation becomes important when there is uncertainty about just what utility should be assigned to given activity mixes, or when it is difficult to project µE into the future, or when Q is a function of time (reflecting technological innovations). The key to formulating an adaptive plan here, paralleling the procedure in other contexts, is continual use of incoming information (about satisfactions and dissatisfactions, changing technology, etc.) to modify activity levels. A well-formulated plan should respond automatically, specifying adjustments needed, as information accumulates. Since, in von Neumann's formulation, the environment is characterized by the utility assigned to different activity vectors, we can limit consideration to payoff-only plans. The fact that reproductive plans are payoff-only plans which can be proved near-optimal (in the sense defined above) for any set of utilities, makes it likely that such plans can supply the responsiveness required here. In  terms the basic problems here, as in the genetics illustration, are the large size of  coupled with nonlinearity and high-dimensionality of µE. Because the concepts of chapters 4 and 5 are formulated in terms of the general framework, they apply here as readily as to genetics. The resulting techniques are specifically interpreted as optimization procedures throughout chapter 6, at the end of section 7.1, and throughout section 7.2. |
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Summarizing: |
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, the set of admissible activity vectors Q. |
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W,transformations of Q into itself. |
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 , plans for selecting a program  , where ct is an activity vector in Q, on the basis of observed utilities {µE(ct'), t' < t}, i.e., payoff-only plans. |
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e, an indexing set of possible utility functions { , }. |
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 , typically a requirement that, for all utility functions µE, , the limiting rate of accrual of a plan, , equal that of the best possible program Cb*(E) in each |
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