Improving learning ability of learning automata using chaos theory

Abstract

A learning automaton (LA) can be considered as an abstract system with a finite set of actions. LA operates by choosing an action from the set of its actions and applying it to the stochastic environment. The environment evaluates the chosen action, and automaton uses the response of the environment to update its decision-making method for selecting the next action. This process is repeated until the optimal action is found. The learning algorithm (learning scheme) determines how to use the environment response for updating the decision-making method to select the next action. In this paper, the chaos theory is incorporated with the LA and a new type of LA, namely chaotic LA (cLA), is introduced. In cLA, the chaotic numbers are used instead of the random numbers when choosing the action. The experiment results show that in most cases, the use of chaotic numbers leads to a significant improvement in the learning ability of the LA. Among the chaotic maps investigated in this paper, the Tent map has better performance than the other maps. The convergence rate/convergence time of the LA will increase/decrease by 91.4%/29.6% to 264.4%/69.1%, on average, by using the Tent map. Furthermore, the chaotic LA has more scalability than the standard LA, and its performance will not decrease significantly by increasing the problem size (number of actions).