A Model of Optimal Behavior in an Unknown Medium

A model of adaptation to an unknown medium in which the learning system has several actions is analyzed, where the medium yields a fixed payoff after each action. The system has a finite learning time and must maximize the sum of the payoffs in that time. The medium is not known beforehand, but a class of media is specified. The given model can be treated as a game in which the strategies are behavior algorithms for the system (which remembers the previously obtained responses of the medium) and the specification, prior to the initiation of operation of the system, of a certain medium from the admissible class of media; the latter strategy is identified with “Nature” as a player. The minimax and maximin points are investigated for the game, and a saddle point is found for a class of mixed strategies.