Active learning methods aim to select the most informative unlabeled instances to label first, and can help to focus image or video annotations on the examples that will most improve a recognition system. However, most existing methods only make myopic queries for a single label at a time, retraining at each iteration. We consider the problem where at each iteration the active learner must select a set of examples meeting a given budget of supervision, where the budget is determined by the funds (or time) available to spend on annotation. We formulate the budgeted selection task as a continuous optimization problem where we determine which subset of possible queries should maximize the improvement to the classifier's objective, without overspending the budget. To ensure far-sighted batch requests, we show how to incorporate the predicted change in the model that the candidate examples will induce. We demonstrate the proposed algorithm on three datasets for object recognition, act...