A Bayesian Formulation of Search, Control and the Exploration/exploitation Trade-oo

A new approach to optimisation is introduced based on a precise probabilistic statement of what is ideally required of an optimisation method. It is convenient to express the formalism in terms of the control of a stationary environment. This leads to an objective function for the controller which uniies the objectives of exploration and exploitation, thereby providing a quantitative principle for managing this trade-oo. This is demonstrated using a variant of the multi-armed bandit problem. This approach opens new possibilities for optimisa-tion algorithms, particularly by using neural network or other adap-tive methods for the adaptive controller. It also opens possibilities for deepening understanding of existing methods. The realisation of these possibilities requires research into practical approximations of the exact formalism.