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In this work, we are interested in presenting a new method for extending specific indices to larger classes of entities, which is obtained by applying some classical results on the extrapolation of real Lipschitz functions to perform a new machine learning procedure. The result is a typical reinforcement learning algorithm based on classical extension theorems for real functions (the McShane-Whitney Theorem) in a new mathematical environment. Following the theoretical part, to show the potential applications of our algorithm, we apply this technique to create a triage automatic system to establish the order of attendance in an emergency service of a hospital based on the professional experience of some doctors.

This is a joint work with A. Ferrer-Sapena, E. Jimenez-Fernandez, E.A. Sanchez-Perez.