In variety of domains such as online advertising and personalized medicine, due to the ever-growing amount of available data, decision makings can be done at a very fine-grained level. This entails treating each individual as a unique item and considering a model for decision rewards based on individual-level features. Parameters of these models are of course unknown to the decision maker and should be learned from data. A successful decision maker balances between exploration (taking actions that are informative about the unknown parameters of the underlying model) and exploitation (taking actions that yields immediate rewards). In this talk, I will discuss this problem in the context of dynamic pricing, where a firm sells a large number of products, described via a wide range of features, to customers that arrive over time. We propose a pricing policy, called Regularized Maximum Likelihood Pricing (RMLP), that obtains asymptotically optimal revenue. Our policy leverages the structure (sparsity) of a high-dimensional demand space in order to obtain a logarithmic regret compared to the clairvoyant policy that knows the parameters of the demand in advance.