Learning preferences on temporal constraints: a preliminary report

A number of reasoning problems involving the manipulation of temporal information can naturally be viewed as implicitly inducing an ordering of potential local decisions involving time (specifically, associated with durations or orderings of events) on the basis of preferences. For example, a pair of events might be constrained to occur in a certain order and, in addition, it might be preferable that the delay between the start times of each of them be as large, or as small, as possible. Sometimes, however, it is more natural to view preferences as something initially ascribed to complete solutions to temporal reasoning problems, rather than to local decisions. For example, in classical scheduling problems, the preference for solutions which minimize makespan is a global, rather than a local, condition. In such cases, it might be useful to learn the local preferences that contribute to globally preferred solutions. This information could be used in heuristics to guide the solver to more promising solutions. To address the potential requirement for information about local preferences, we propose to apply learning techniques to infer local preferences from global ones. The preliminary work proposes an approach based on the notion of learning a set of soft temporal constraints, given a training set of solutions to a Temporal CSP, and an objective function for evaluating each solution in the set.