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In this letter, we have found a more general formulation of the REward Increment = Nonnegative Factor times Offset Reinforcement times Characteristic Eligibility (REINFORCE) learning principle first suggested by Williams. The new formulation has enabled us to apply the principle to global reinforcement learning in networks with various sources of randomness, and to suggest several simple local rules for such networks. Numerical simulations have shown that for simple classification and reinforcement learning tasks, at least one family of the new learning rules gives results comparable to those provided by the famous Rules Ar-i and Ar-p for the Boltzmann machines