Abstract: We present Epoch-Greedy, an algorithm for multi-armed bandits with observable side information. Epoch-Greedy has the following properties: No knowledge of a time horizon $T$ is necessary. The regret incurred by Epoch-Greedy is controlled by a sample complexity bound for a hypothesis class. The regret scales as $O(T^{2/3} S^{1/3})$ or better (sometimes, much better). Here $S$ is the complexity term in a sample complexity bound for standard supervised learning.