Learning Automata (LA) is a popular decision making mechanism to "determine the optimal action out of a set of allowable actions" [1]. The distinguishing characteristic of automata-based learning is that the search for the optimising parameter vector is conducted in the space of probability distributions defined over the parameter space, rather than in the parameter space itself [2]. Recently, Goodwin and Yazidi pioneered the use of Ant Colony Optimisation (ACO) for solving classification problems [3]. In this paper, we propose a novel classifier based on the theory of LA. The classification problem is formulated as a deterministic optimization problem involving a team of LA that operate collectively to optimize an objective function.Although many LA algorithms have been devised in the literature, those LA schemes are not able to solve deterministic optimization problems as they suppose that the environment is stochastic. In this paper, we develop a novel pursuit LA which can be seen as the counterpart of the family of pursuit LA developed for stochastic environments [4]. While classical pursuit LA are able to pursue the action with the highest reward estimate, our pursuit LA rather pursues the collection of actions that yield the highest performance. The theoretical analysis of the pursuit scheme does not follow classical LA proofs and can pave the way towards more schemes where LA can be applied to solve deterministic optimization problems.When applied to classification, the essence of our scheme is to search for a separator in the feature space by imposing a LA based random walk in a