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We have found a more general formulation of the REINFORCE learning principle which had been proposed by R. J. Williams for the case of artificial neural networks with stochastic cells ("Boltzmann machines"). This formulation has enabled us to apply the principle to global reinforcement learning in networks with deterministic neural cells but stochastic synapses, and to suggest two groups of new learning rules for such networks, including simple local rules. Numerical simulations have shown that at least for several popular benchmark problems one of the new learning rules may provide results on a par with the best known global reinforcement techniques.
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