An Autonomous Physical System (APS) will be expected to reliably and independently evaluate, execute, and achieve goals while respecting surrounding rules, laws, or conventions. In doing so, an APS must rely on a broad spectrum of dynamic, complex, and often imprecise information about its surroundings, the task it is to perform, and its own sensors and actuators. For example, cleaning in a home or commercial setting requires the ability to perceive, grasp, and manipulate many physical objects, the ability to reliably perform a variety of subtasks such as washing, folding, and stacking, and knowledge about local conventions such as how objects are classified and where they should be stored. The information required for reliable autonomous operation may come from external sources and from the robot's own sensor observations or in the form of direct instruction by a trainer. Similar considerations apply across many domains - construction, manufacturing, in-home assistance, and healthcare. For example, surgeons spend many years learning about physiology and anatomy before they touch a patient. They then perform roughly 1000 surgeries under the tutelage of an expert surgeon, and they practice basic maneuvers such as suture tying thousands of times outside the operating room. All of these elements come together to achieve expertise at this task. Endowing a system with robust autonomy by traditional programming methods has thus far had limited success. Several promising new paths to acquiring and processing such data are emerging. This white paper outlines three promising research directions for enabling an APS to learn the physical and information skills necessary to perform tasks with independence and flexibility: Deep Reinforcement Learning, Human-Robot Interaction, and Cloud Robotics.