  For a learning automaton, a proper configuration of its learning parameters,
which are crucial for the automaton's performance, is relatively difficult due
to the necessity of a manual parameter tuning before real applications. To
ensure a stable and reliable performance in stochastic environments, parameter
tuning can be a time-consuming and interaction-costing procedure in the field
of LA. Especially, it is a fatal limitation for LA-based applications where the
interactions with environments are expensive.
  In this paper, we propose a parameter-free learning automaton scheme to avoid
parameter tuning by a Bayesian inference method. In contrast to existing
schemes where the parameters should be carefully tuned according to the
environment, the performance of this scheme is not sensitive to external
environments because a set of parameters can be consistently applied to various
environments, which dramatically reduce the difficulty of applying a learning
automaton to an unknown stochastic environment. A rigorous proof of
$\epsilon$-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 parameter-free learning automaton (PFLA) can achieve a competitive
performance compared with other well-tuned schemes and outperform untuned
schemes on consistency of performance.
