In recent years, ideas from the computational field of reinforcement learning have revolutionized the study of learning in the brain, famously providing new, precise theories of how dopamine affects learning in the basal ganglia. However, reinforcement learning algorithms are notorious for not scaling well to multidimensional environments, as is required for real-world learning. We hypothesized that the brain naturally reduces the dimensionality of real-world problems to only those dimensions that are relevant to predicting reward, and conducted an experiment to assess by what algorithms and with what neural mechanisms this "representation learning" process is realized in humans. Our results suggest that a bilateral attentional control network comprising the intraparietal sulcus, precuneus, and dorsolateral prefrontal cortex is involved in selecting what dimensions are relevant to the task at hand, effectively updating the task representation through trial and error. In this way, cortical attention mechanisms interact with learning in the basal ganglia to solve the "curse of dimensionality" in reinforcement learning.