Adaptive systems for prediction problems
The paper investigates classes of adaptive systems used as prediction machines in certain simple games. Ideally the machine should approach a state which will maximize its expected gain. The simplest machine takes the form of an urn, similar to the urn models of Polya and Friedman, but modified so as to form an adaptive system. The machine is characterized by learning parameters and a reinforcement scheme. The simplest machine is then extended to a machine with 2 to the nth power urns, each urn corresponding to one of the possible n-tuples of previous moves. This machine is further generalized to a machine which begins as a one-urn machine and splits states as information is accumulated. This machine is capable of growing until it comprises any number of urns. Many of these machines were simulated on a computer, playing against a variety of opponents. These results indicate that the prediction is not optimal but is considerably better than random guessing. A heuristic value of the limiting state for the one urn machine playing against a probabilistic opponent is obtained and the results of the simulation support this value. No convergence proof is available except for restricted values of the parameters alpha and beta. (Author).
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