  Learning Automata (LA) are considered as one of the most powerful tools in
the field of reinforcement learning. The family of estimator algorithms is
proposed to improve the convergence rate of LA and has made great achievements.
However, the estimators perform poorly on estimating the reward probabilities
of actions in the initial stage of the learning process of LA. In this
situation, a lot of rewards would be added to the probabilities of non-optimal
actions. Thus, a large number of extra iterations are needed to compensate for
these wrong rewards. In order to improve the speed of convergence, we propose a
new P-model absorbing learning automaton by utilizing a double competitive
strategy which is designed for updating the action probability vector. In this
way, the wrong rewards can be corrected instantly. Hence, the proposed Double
Competitive Algorithm overcomes the drawbacks of existing estimator algorithms.
A refined analysis is presented to show the $\epsilon-optimality$ of the
proposed scheme. The extensive experimental results in benchmark environments
demonstrate that our proposed learning automata perform more efficiently than
the most classic LA $SE_{RI}$ and the current fastest LA $DGCPA^{*}$.
