A Model to Study Phase Transition and Plateaus in Relational Learning

The feasibility of symbolic learning strongly relies on the efficiency of heuristic search in the hypothesis space. However, recent works in relational learning claimed that the phase transition phenomenon which may occur in the subsumption test during search acts as a plateau for the heuristic search, strongly hindering its efficiency. We further develop this point by proposing a learning problem generator where it is shown that top-down and bottom-up learning strategies face a plateau during search before reaching a solution. This property is ensured by the underlying CSP generator, the RB model, that we use to exhibit a phase transition of the subsumption test. In this model, the size of the current hypothesis maintained by the learner is an order parameter of the phase transition and, as it is also the control parameter of heuristic search, the learner has to face a plateau during the problem resolution. One advantage of this model is that small relational learning problems with interesting properties can be constructed and therefore can serve as a benchmark model for complete search algorithms used in learning. We use the generator to study complete informed and non-informed search algorithms for relational learning and compare their behaviour when facing a phase transition of the subsumption test. We show that this generator exhibits the pathological case where informed learners degenerate into non-informed ones.