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).

中文翻译：

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利用混沌理论提高学习自动机的学习能力

学习自动机 (LA) 可以被视为具有有限动作集的抽象系统。LA 通过从其动作集中选择一个动作并将其应用于随机环境来运行。环境评估选择的动作，自动机使用环境的响应来更新其选择下一个动作的决策方法。重复此过程，直到找到最佳动作。学习算法（learning scheme）决定了如何利用环境响应来更新决策方法来选择下一步行动。本文将混沌理论与LA相结合，介绍了一种新型的LA，即混沌LA（cLA）。在 cLA 中，选择动作时使用混沌数而不是随机数。实验结果表明，在大多数情况下，混沌数的使用导致 LA 学习能力的显着提高。在本文研究的混沌地图中，帐篷地图的性能优于其他地图。通过使用帐篷地图，LA 的收敛速度/收敛时间平均会增加/减少 91.4%/29.6% 到 264.4%/69.1%。此外，混沌 LA 比标准 LA 具有更多的可扩展性，其性能不会因问题规模（动作数量）的增加而显着下降。