Swarm intelligence to coordinate decentralized learning automata in identical payoff games

Abstract

Decentralized learning automata (DLA) consist of a large number of learning automata (LAs), which learn independently without information exchange among them. However, although these LAs are able to reach Nash equilibrium theoretically, their learning efficiencies are weakened drastically since each LA works under nonstationary environment instead of stationary environment. In order to coordinate different LAs in DLA, swarm intelligence is an appropriate mechanism that can help all LAs to make swarm decision. As a representative of swarm intelligence algorithms, particle swarm optimization (PSO) can complete this goal. PSO derives from simulating the behavior of flying birds and has shown effective swarm intelligence by cooperation among the particles. It is very easy to implement and owns very little computational and memory overhead. This work utilizes PSO to provide an appropriate coordination mechanism in DLA through swarm intelligence, called learning automata swarm optimization (LASO). The PSO's swarm best (gbest) is treated as swarm decision, which is used by LASO as "optimal" estimator information, then all LAs utilize it to update their selection probability vectors. Next, the proposed LASO is applied in identical payoff games and constructs a model to solve them effectively. In our model, a PSO with equal resampling and top-N additional re-evaluations (PSO-ERN) algorithm is used to estimate the matrix of game's reward probabilities since its stochastic causes multiple estimations of the same play to result in different environmental responses. Computational experiments in identical payoff games demonstrate the fast and accurate convergence of LASO over the existing DLA.