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Object delivery by pushing objects with mobile robots on a flat surface has been successfully demonstrated. However, existing methods can push objects that have a circular or rectangular shape. In this paper, we introduce a learning-based approach for pushing objects of any irregular shape to user-specified goal locations. We first automatically collect a set of data on how an irregular-shaped object moves given the robot's relative position and pushing direction. We collect this data with a randomized approach, and we demonstrate that this approach can successfully collect useful data. Object delivery is achieved by using the collected data with a non-parametric regression method. We demonstrate our approach with a number of irregular-shaped objects.