There are many applications in which it is desirable to order rather than classify instances. Here we consider the problem of learning how to order, given feedback in the form of preference judgments, i.e., statements to the effect that one instance should be ranked ahead of another. We outline a two-stage approach in which one first learns by conventional means a preference function, of the form PREF(u; v), which indicates whether it is advisable to rank u before v. New instances are then ordered so as to maximize agreements with the learned preference function. We show that the problem of finding the ordering that agrees best with a preference function is NP-complete, even under very restrictive assumptions. Nevertheless, we describe a simple greedy algorithm that is guaranteed to find a good approximation. We then discuss an on-line learning algorithm, based on the "Hedge" algorithm, for finding a good linear combination of ranking "experts." We use the ordering algorith...
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