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In this paper, we explore how to efficiently combine crowdsourcing and machine intelligence for the problem of document screening, where we need to screen documents with a set of machine-learning filters. Specifically, we focus on building a set of machine learning classifiers that evaluate documents, and then screen them efficiently. It is a challenging task since the budget is limited and there are countless number of ways to spend the given budget on the problem. We propose a multi-label active learning screening specific sampling technique -- objective-aware sampling -- for querying unlabelled documents for annotating. Our algorithm takes a decision on which machine filter need more training data and how to choose unlabeled items to annotate in order to minimize the risk of overall classification errors rather than minimizing a single filter error. We demonstrate that objective-aware sampling significantly outperforms the state of the art active learning sampling strategies.