  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
instances 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 binary
preference function indicating whether it is advisable to rank one instance
before another. Here we consider an on-line algorithm for learning preference
functions that is based on Freund and Schapire's 'Hedge' algorithm. In the
second stage, new instances are ordered so as to maximize agreement with the
learned preference function. We show that the problem of finding the ordering
that agrees best with a learned preference function is NP-complete.
Nevertheless, we describe simple greedy algorithms that are guaranteed to find
a good approximation. Finally, we show how metasearch can be formulated as an
ordering problem, and present experimental results on learning a combination of
'search experts', each of which is a domain-specific query expansion strategy
for a web search engine.
