The author states and proves asymptotic results concerning various variable structure stochastic automata. These automata, however, unlike the automata discussed in the literature, change the action probabilities in discrete jumps. The automata are called linear or nonlinear depending on whether these jumps are all of equal length. The DL//R //I (discretized linear reward--inaction) and DN//R //I (discretized nonlinear reward--inaction) schemes are shown to be epsilon -optimal. The DL//I //P (discretized linear inaction penalty) scheme is shown to be ergodic and expedient. By artificially making the end states of the latter automata absorbing, the author has designed the ADL//I //P (absorbing discretized linear inaction penalty) automaton and proven its epsilon -optimality. He also presents simulation results for the discretized linear reward-penalty scheme and based on these, conjectures that the scheme is epsilon -optimal.

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Conference IEEE 1985 Proceedings of the International Conference on Cybernetics and Society.
Citation
Oommen, J. (1985). LINEAR AND NONLINEAR ABSORBING AND ERGODIC DISCRETIZED TWO ACTION LEARNING AUTOMATA. In IEEE 1985 Proceedings of the International Conference on Cybernetics and Society. (pp. 241–245).