Reinforcement and error-based processes are essential for motor learning, with the cerebellum thought to be required only for the error-based mechanism. Here we examined learning and retention of a reaching skill under both processes. Control subjects learned similarly from reinforcement and error-based feedback, but showed much better retention under reinforcement. To apply reinforcement to cerebellar patients, we developed a closed-loop reinforcement schedule in which task difficulty was controlled based on recent performance. This schedule produced substantial learning in cerebellar patients and controls. Cerebellar patients varied in their learning under reinforcement but fully retained what was learned. In contrast, they showed complete lack of retention in error-based learning. We developed a mechanistic model of the reinforcement task and found that learning depended on a balance between exploration variability and motor noise. While the cerebellar and control groups had similar exploration variability, the patients had greater motor noise and hence learned less. Our results suggest that cerebellar damage indirectly impairs reinforcement learning by increasing motor noise, but does not interfere with the reinforcement mechanism itself. Therefore, reinforcement can be used to learn and retain novel skills, but optimal reinforcement learning requires a balance between exploration variability and motor noise.