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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alpha and beta alpha-beta pruning alternative amalgamation approach associated assumption Bayes Bayes estimate board positions calculated cards marked checkers chess coefficient conditional probabilities considered counters cup machine U(3,l,l CUP2 CUPNUM Curve of U(3,l,l defined denoted determine discussed environment equation U.l6 evaluation expected finite state machine four cup machine fraction of heads function game matrix game of penny game theory game tree Hence initial input INTEGER large number learning curve learning mechanism look-ahead machine converges machine had won machine plays machine winning machine's Markov Markov chain memory mixed strategy mutational number of head number of moves opponent's optimal strategy outcome output parameters alpha payoffs penny matching machine plane player plays randomly possible predict proba probabilistic probability distribution procedure random numbers random variable RANF region Section SEER sensory units sequence of moves shown in Figure splitting machine SUBROUTINE symbol tail cards urn models values vector Versus an Opponent