Optimality in motor control

Several models of human motor control propose that stereotypical movements like reaching are optimal, in the sense that they minimize a performance cost function. However, from a computational point of view, optimal control is a hard problem. First, most natural bio-mechanical systems are redundant—there are more degrees of freedom than required. Second, optimal control tasks often suffer from the "curse of dimensionality". For example, consider moving a two-joint arm from location A to location B in 100 time steps. If torques are discretized to one of 10 values, then there are 10200 possible torque sequences. How do we efficiently search a space of that size? In this thesis we try to answer some of these questions arising from a theory of optimal control. First, if optimal control is hard, how do humans accurately solve day to day control problems? We propose that for stereotypical movements like reaching, the optimal control solution can be decomposed as a sum of scaled and time shifted components, or "motor synergies". In one project, we discover these synergies through dimensionality reduction. Near-optimal control is achieved by linearly combining the synergies we discovered. In a second project, synergies are solutions to representative motor tasks. We show that libraries of such synergies provide overcomplete representations of the space of motor solutions. Control solutions for new tasks are found through a greedy additive regression procedure that tends to linearly combine a small number of synergies from the library. Second, we conducted experiments to show that humans are able to perform well even under certain non-stereotypical control regimes. In these experiments, subjects were required to control a dynamical system corrupted with noise. A comparison of human performance to the theoretically optimal solution shows that humans reach close to optimal performance under a variety of noise conditions. Additionally, we showed that subjects adapt to the noise regime rather than using a fixed controller across different noise conditions. Finally, we propose a theoretical learning model inspired from behavioral shaping, which is an incremental training procedure commonly used to teach complex behaviors. In shaping, the learner is rewarded for performing successively difficult tasks that monotonically provide better approximations to the target task. We formulate shaping in the context of a search problem. In a search problem, the learner has to use a membership oracle of a concept to find one positive instance of the concept. In a shaped search problem, the learner has access to a sequence of membership oracles of increasingly restrictive concepts leading to the final concept. For the concept class of intervals, we show that the search problem can be solved with an exponentially smaller number of samples if a such a sequence is used. Additionally, we prove that convexity of concepts is important for shaping to be successful.