For better or worse, humans live a resource constrained existence; only a fraction of the sensations our body experiences ever reach conscious awareness, and we store a shockingly small subset of these experiences in short-term memory for later use. Despite these observations, most theories of learning assume that, given feedback about a new experience, knowledge is updated so as to minimize subsequent errors with minimal consideration of cognitive capacity constraints. Acknowledging that human cognition has clear biological limitations, we explored the degree to which human learning could be better described with sets of biases toward simpler and more parsimonious mental representations (i.e., simplicity biases) relative to an error-driven, accuracy-maximizing normative model. Taking the normative model as a basis, we developed a suite of nested computational models that use various mechanistic simplicity biases to explain learning. We fit these models to four data sets that varied in the type of learning needed to achieve high accuracy. Across all data sets, we found consistent evidence that the best descriptors of human learning were models with mechanisms that instantiated a constrained optimization process, where errors were minimized subject to constraints on both attention and memory. Importantly, whereas normative models failed to account for patterns of attentional deployment over time, models with simplicity biases accounted well for both choice responses and fixation data as participants learned various categorization tasks.