A new class of learning automata for selecting an optimal subset

Interacting with a random environment, Learning Automata (LAs) are automata that, generally, have the task of learning the optimal action based on responses from the environment. Distinct from the traditional goal of Learning Automata to select only the optimal action out of a set of actions, this paper considers a multiple-action selection problem and proposes a novel class of Learning Automata for selecting an optimal subset of actions. Their objective is to identify the optimal subset: the top k out of r actions. Based on conventional continuous pursuit and discretized pursuit learning schemes, this paper introduces four pursuit learning schemes for selecting the optimal subset, called continuous equal pursuit, discretized equal pursuit, continuous unequal pursuit and discretized unequal pursuit learning schemes, respectively. In conjunction with a reward-inaction learning paradigm, the above four schemes lead to four versions of pursuit Learning Automata for selecting the optimal subset. The simulation results present a quantitative comparison between them.