The growing availability of high throughput measurement devices in the operating room makes possible the collection of a huge amount of data about the state of the patient and the doctors? practice during a surgical operation. This paper explores the possibility of extracting from these data relevant information and pertinent decision rules in order to support the daily anesthesia procedures. In particular we focus on machine learning strategies to design a closed-loop controller that, in a near future, could play the role of a decision support tool and, in a further perspective, the one of automatic pilot of the anesthesia procedure. Two strategies (direct and inverse) for learning a controller from observed data are assessed on the basis of a database of measurements collected in recent years by the ULB Erasme anaesthesiology group. The preliminary results of the learning approach applied to the regulation of hypnosis through the bispectral index (BIS) in a simulated framework appear to be promising and worthy of future investigation.