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We consider the problem of learning good trajectories for manipulation tasks.This is challenging because the criterion defining a good trajectory varieswith users, tasks and environments. In this paper, we propose a co-activeonline learning framework for teaching robots the preferences of its users forobject manipulation tasks. The key novelty of our approach lies in the type offeedback expected from the user: the human user does not need to demonstrateoptimal trajectories as training data, but merely needs to iteratively providetrajectories that slightly improve over the trajectory currently proposed bythe system. We argue that this co-active preference feedback can be more easilyelicited from the user than demonstrations of optimal trajectories, which areoften challenging and non-intuitive to provide on high degrees of freedommanipulators. Nevertheless, theoretical regret bounds of our algorithm matchthe asymptotic rates of optimal trajectory algorithms. We demonstrate thegeneralizability of our algorithm on a variety of grocery checkout tasks, forwhom, the preferences were not only influenced by the object being manipulatedbut also by the surrounding environment.\footnote{For more details and ademonstration video, visit: \url{http://pr.cs.cornell.edu/coactive}}

Learning Trajectory Preferences for Manipulators via Iterative Improvement