Learning Automata
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A learning automaton is one type of machine learning algorithm studied since 1970s. Learning automata select their current action based on past experiences from the environment. It will fall into the range of reinforcement learning if the environment is
stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...
and a Markov decision process (MDP) is used.


History

Research in learning automata can be traced back to the work of
Michael Lvovitch Tsetlin Michael Lvovitch Tsetlin (the surname is also written Cetlin, Tzetlin, Zeitlin, Zetlin; cyrillic: Михаил Львович Цетлин) (22 September 1924 – 30 May 1966) was a Soviet mathematician and physicist who worked on cybernetics. He i ...
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.


Definition

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. Formally, Narendra and Thathachar define a stochastic automaton to consist of: * a set ''X'' of possible inputs, * a set Φ = of possible internal states, * a set α = of possible outputs, or actions, with ''r'' ≤ ''s'', * an initial state probability vector ''p(0)'' = ≪ ''p''1(0), ..., ''p''''s''(0) ≫, * a computable function ''A'' which after each time step ''t'' generates ''p''(''t''+1) from ''p''(''t''), the current input, and the current state, and * a function ''G'': Φ → α which generates the output at each time step. In their paper, they investigate only stochastic automata with ''r'' = ''s'' and ''G'' being bijective, allowing them to confuse actions and states. The states of such an automaton correspond to the states of a "discrete-state discrete-parameter Markov process". At each time step ''t''=0,1,2,3,..., the automaton reads an input from its environment, updates ''p''(''t'') to ''p''(''t''+1) by ''A'', randomly chooses a successor state according to the probabilities ''p''(''t''+1) and outputs the corresponding action. The automaton's environment, in turn, reads the action and sends the next input to the automaton. Frequently, the input set ''X'' = is used, with 0 and 1 corresponding to a ''nonpenalty'' and a ''penalty'' response of the environment, respectively; in this case, the automaton should learn to minimize the number of ''penalty'' responses, and the feedback loop of automaton and environment is called a "P-model". More generally, a "Q-model" allows an arbitrary finite input set ''X'', and an "S-model" uses the interval ,1of
real numbers In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...
as ''X''. A visualised demo / Art Work of a single Learning Automaton had been developed by µSystems (microSystems) Research Group at Newcastle University.


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.


See also

* Reinforcement learning *
Game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
* Automata theory


Literature

* Philip Aranzulla and John Mellor