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No Free Lunch in Ball Catching: A Comparison of Cartesian and Angular Representations for Control

Höfer, Sebastian; Raisch, Jörg; Toussaint, Marc; Brock, Oliver

How to run most effectively to catch a projectile, such as a baseball, that is flying in the air for a long period of time? The question about the best solution to the ball catching problem has been subject to intense scientific debate for almost 50 years. It turns out that this scientific debate is not focused on the ball catching problem alone, but revolves around the research question what constitutes the ingredients of intelligent decision making. Over time, two opposing views have emerged: the generalist view regarding intelligence as the ability to solve any task without knowing goal and environment in advance, based on optimal decision making using predictive models; and the specialist view which argues that intelligent decision making does not have to be based on predictive models and not even optimal, advocating simple and efficient rules of thumb (heuristics) as superior to enable accurate decisions. We study two types of approaches to the ball catching problem, one for each view, and investigate their properties using both a theoretical analysis and a broad set of simulation experiments. Our study shows that neither of the two types of approaches can be regarded as superior in solving all relevant variants of the ball catching problem: each approach is optimal under a different realistic environmental condition. Therefore, predictive models neither guarantee nor prevent success a priori, and we further show that the key difference between the generalist and the specialist approach to ball catching is the type of input representation used to control the agent. From this finding, we conclude that the right solution to a decision making or control problem is orthogonal to the generalist and specialist approach, and thus requires a reconciliation of the two views in favor of a representation-centric view.