As visual recognition scales up to ever larger numbers of categories, maintaining high accuracy is increasingly difficult. In this work, we study the problem of optimizing accuracy-specificity trade-offs in large scale recognition, motivated by the observation that object categories form a semantic hierarchy consisting of many levels of abstraction. A classifier can select the appropriate level, trading off specificity for accuracy in case of uncertainty. By optimizing this trade-off, we obtain classifiers that try to be as specific as possible while guaranteeing an arbitrarily high accuracy. We formulate the problem as maximizing information gain while ensuring a fixed, arbitrarily small error rate with a semantic hierarchy. We propose the Dual Accuracy Reward Trade-off Search (DARTS) algorithm and prove that, under practical conditions, it converges to an optimal solution. Experiments demonstrate the effectiveness of our algorithm on datasets ranging from 65 to over 10,000 categories.