  We propose Coactive Learning as a model of interaction between a learning
system and a human user, where both have the common goal of providing results
of maximum utility to the user. At each step, the system (e.g. search engine)
receives a context (e.g. query) and predicts an object (e.g. ranking). The user
responds by correcting the system if necessary, providing a slightly improved
-- but not necessarily optimal -- object as feedback. We argue that such
feedback can often be inferred from observable user behavior, for example, from
clicks in web-search. Evaluating predictions by their cardinal utility to the
user, we propose efficient learning algorithms that have ${\cal
O}(\frac{1}{\sqrt{T}})$ average regret, even though the learning algorithm
never observes cardinal utility values as in conventional online learning. We
demonstrate the applicability of our model and learning algorithms on a movie
recommendation task, as well as ranking for web-search.
