Although the field of Learning Automata (LA) has made significant progress in the last four decades, the LA-based methods to tackle problems involving environments with a large number of actions are, in reality, relatively unresolved. The extension of the traditional LA (fixed structure, variable structure, discretized, and pursuit) to problems within this domain cannot be easily established when the number of actions is very large. This is because the dimensionality of the action probability vector is correspondingly large, and consequently, most components of the vector will, after a relatively short time, have values that are smaller than the machine accuracy permits, implying that they will never be chosen. This paper pioneers a solution that extends the continuous pursuit paradigm to such large-actioned problem domains. The beauty of the solution is that it is hierarchical, where all the actions offered by the environment reside as leaves of the hierarchy. Further, at every level, we merely require a two-action LA which automatically resolves the problem of dealing with arbitrarily small action probabilities. Additionally, since all the LA invoke the pursuit paradigm, the best action at every level trickles up towards the root. Thus, by invoking the property of the “max” operator, in which, the maximum of numerous maxima is the overall maximum, the hierarchy of LA converges to the optimal action. Apart from reporting the theoretical properties of the scheme, the paper contains extensive experimental results which demonstrate the power of the scheme and its computational advantages. As far as we know, there are no comparable results in the field of LA.