A parameter-free learning automaton scheme

For a learning automaton, a proper configuration of the learning parameters is crucial. To ensure stable and reliable performance in stochastic environments, manual parameter tuning is necessary for existing LA schemes, but the tuning procedure is time-consuming and interaction-costing. It is a fatal limitation for LA-based applications, especially for those environments where the interactions are expensive. In this paper, we propose a parameter-free learning automaton (PFLA) scheme to avoid parameter tuning by a Bayesian inference method. In contrast to existing schemes where the parameters must be carefully tuned according to the environment, PFLA works well with a set of consistent parameters in various environments. This intriguing property dramatically reduces the difficulty of applying a learning automaton to an unknown stochastic environment. A rigorous proof of ϵ-optimality for the proposed scheme is provided and numeric experiments are carried out on benchmark environments to verify its effectiveness. The results show that, without any parameter tuning cost, the proposed PFLA can achieve a competitive performance compared with other well-tuned schemes and outperform untuned schemes on the consistency of performance.