Is the assumption that people automatically know their own preferences innocuous? We present an experiment studying the limits of preference discovery. If tastes must be learned through experience, preferences for some goods may never be learned because it is costly to try new things, and thus non-learned preferences may cause welfare loss. We conduct an online experiment in which finite-lived participants have an induced utility function over fictitious goods about whose marginal utilities they have initial guesses. Subjects learn most, but not all, of their preferences eventually. Choice reversals occur, but primarily in early rounds. Subjects slow their sampling of new goods over time, supporting our conjecture that incomplete learning can persist. Incomplete learning is more common for goods that are rare, have low initial value guesses, or appear in choice sets alongside goods that appear attractive. It is also more common for people with lower incomes or shorter lifetimes. More noise in initial value guesses has opposite effects for low-value and high-value goods because it affects the perceived likelihood that the good is worth trying. Over time, subjects develop a pessimistic bias in beliefs about goods’ values, since optimistic errors are more likely to be corrected. Overall, our results show that if people need to learn their preferences through consumption experience, that learning process will cause choice reversals, and even when a person has completed sampling the goods she is willing to try, she may continue to lose welfare because of suboptimal choices that arise from non-learned preferences.