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This paper is concerned with the application of reinforcement learning to the stochastic optimal control of an idealized active vehicle suspension system. The use of learning automata in optimal control is a new application of this machine learning technique, and the principal aim of this work is to define and demonstrate the method in a relatively simple context, as well as to compare performance against results obtained from standard linear optimal control theory. The most distinctive feature of the approach is that no formal modelling is involved in the control system design; once implemented, learning takes place on-line, and the automaton improves its control performance with respect to a predefined cost function. An important new feature of the method is the use of subset actions, which enables the automaton to reduce the size of its action set at any particular instant, without imposing any global restrictions on the controller that is eventually learnt. The results, though based on simulation studies, suggest that there is great potential for implementing learning control in active vehicle suspensions, as well as for many other systems.