Constraints on underspecified target trajectories

Much of the recent interest in artificial neural networks is founded on the development of supervised learning algorithms for nonlinear problems [1, 30, 39, 42, 47]. These algorithms, the most well-known being backpropagation, are able to model a large class of nonlinear transformations by assigning credit to internal “hidden” units. The remaining units—those connected directly to the environment—are generally assumed to be provided with target states. This assumption appears to be a liability; it is by no means clear that such desired outputs can always be provided. Consider, for example, a network serving as a feedforward controller for a robot. Such a network must produce torques as a function of the environmental goal and the current state of the robot. In general, however, the environment provides only the goal and not the torques that achieve the goal. Furthermore, if we assume the existence of an oracle that provides the torques as training data, then there appears to be little reason (other than perhaps speed) not to use the oracle as the controller in place of the network.