Feedback signals may be of different modality, latency, and accuracy. To learn and control motor tasks, the feedback available may be redundant, and it would not be necessary to rely on every accessible feedback loop. Which feedback loops should then be utilized? In this article, we propose that the latency is a critical factor to determine which signals will be influential at different learning stages. We use a computational framework to study the role of feedback modules with different latencies in optimal motor control. Instead of explicit gating between modules, the reinforcement learning algorithm learns to rely on the more useful module. We tested our paradigm for two different implementations, which confirmed our hypothesis. In the first, we examined how feedback latency affects the competitiveness of two identical modules. In the second, we examined an example of visuomotor sequence learning, where a plastic, faster somatosensory module interacts with a preacquired, slower visual module. We found that the overall performance depended on the latency of the faster module alone, whereas the relative latency determines the independence of the faster from the slower. In the second implementation, the somatosensory module with shorter latency overtook the slower visual module, and realized better overall performance. The visual module played different roles in early and late learning. First, it worked as a guide for the exploration of the somatosensory module. Then, when learning had converged, it contributed to robustness against system noise and external perturbations. Overall, these results demonstrate that our framework successfully learns to utilize the most useful available feedback for optimal control.