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Distributed manipulators - consisting of a set of actuators or robots working cooperatively to achieve a manipulation task - are robust and flexible tools for performing a range of planar manipulation skills. One novel example is the delta array, a distributed manipulator composed of a grid of delta robots, capable of performing dexterous manipulation tasks using strategies incorporating both dynamic and static contact. Hand-designing effective distributed control policies for such a manipulator can be complex and time consuming, given the high-dimensional action space and unfamiliar system dynamics. In this paper, we examine the principles guiding development and control of such a delta array for a planar translation task. We explore policy learning as a robust cooperative control approach, allowing for smooth manipulation of a range of objects, showing improved accuracy and efficiency over baseline human-designed policies.