Developers often need to use appropriate APIs to program efficiently, but it is usually a difficult task to identify the exact one they need from a vast of candidates. To ease the burden, a multitude of API recommendation approaches have been proposed. However, most of the currently available API recommenders do not support the effective integration of users' feedback into the recommendation loop. In this paper, we propose a framework, BRAID (Boosting RecommendAtion with Implicit FeeDback), which leverages learning-to-rank and active learning techniques to boost recommendation performance. By exploiting users' feedback information, we train a learning-to-rank model to re-rank the recommendation results. In addition, we speed up the feedback learning process with active learning. Existing query-based API recommendation approaches can be plugged into BRAID. We select three state-of-the-art API recommendation approaches as baselines to demonstrate the performance enhancement of BRAID measured by Hit@k (Top-k), MAP, and MRR. Empirical experiments show that, with acceptable overheads, the recommendation performance improves steadily and substantially with the increasing percentage of feedback data, comparing with the baselines.