A branch of the theory of adaptive control is devoted to learning automata surveyed by Narendra and Thathachar which were originally described explicitly as finite state automata. Learning automata select their current action based on past experiences from the environment.
Research in learning automata can be traced back to the work of Tsetlin in the early 1960s in the Soviet Union. Together with some colleagues, he published a collection of papers on how to use matrices to describe automata functions. Additionally, Tsetlin worked on reasonable and collective automata behaviour, and on automata games. Learning automata were also investigated by researches in the United States in the 1960s. However, the term learning automaton was not used until Narendra and Thathachar introduced it in a survey paper in 1974.
A learning automaton is an adaptive decision-making unit situated in a random environment that learns the optimal action through repeated interactions with its environment. The actions are chosen according to a specific probability distribution which is updated based on the environment response the automaton obtains by performing a particular action.
With respect to the field of reinforcement learning, learning automata are characterized as policy iterators. In contrast to other reinforcement learners, policy iterators directly manipulate the policy π. Another example for policy iterators are evolutionary algorithms.
Finite action-set learning automata 
Finite action-set learning automata (FALA) are a class of learning automata for which the number of possible actions is finite or, in more mathematical terms, for which the size of the action-set is finite.
Philip Aranzulla and John Mellor.
Narendra K., Thathachar M.A.L., learning automata – a survey, IEEE Transactions on Systems, Man, and Cybernetics, July 1974, Vol. SMC-4, No. 4, pp. 323–334.
Mikhail L’vovich TSetlin., Automaton Theory and the Modelling of Biological Systems, New York and London, Academic Press, 1973. (Find in a library)
See also 
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