We study a family of stylized assortment planning problems, where arriving customers make purchase decisions among offered products based on maximizing their utility. Given limited display capacity and no a priori information on consumers' utility, the retailer must select which subset of products to offer. By offering different assortments and observing the resulting purchase behavior, the retailer learns about consumer preferences, but this experimentation should be balanced with the goal of maximizing revenues. We develop a family of dynamic policies that judiciously balance the aforementioned tradeoff between exploration and exploitation, and prove that their performance cannot be improved upon in a precise mathematical sense. One salient feature of these policies is that they "quickly" recognize, and hence limit experimentation on, strictly suboptimal products.