Predators must use the appearance of their prey to decide whether it is likely to be defended. Most theory assumes that predators have completed learning about prey appearance, yet we do not understand how predators learn which aspects of appearance to use for classifying prey. If sampling prey can be risky, predators might forgo opportunities to learn about the relationship between prey appearance and defense. Using Bayesian inference and dynamic programming, we modeled how the immediate risks and future rewards of learning about prey appearance influence how predators learn. In addition, we explored how variation in predator learning affects the evolution of mimicry, which occurs when two prey evolve to share a common signal to predators. We found that when learning about prey with distinct appearances was expensive, optimal predators tended to lump them into the same category or exhibit an unwillingness to sample at all (neophobia). This resulted in a reduction in selection for defensive mimicry. However, the same predator behavior favored the evolution of aggressive mimicry, because in that case, mimics benefited from being sampled. When prey were very rare and costs of sampling them were high, predators exhibited neophobia, refusing to attack. This behavior could forestall the evolution of mimicry and instead select for polymorphism.