  Weakly-supervised object detection (WSOD) has emerged as an inspiring recent
topic to avoid expensive instance-level object annotations. However, the
bounding boxes of most existing WSOD methods are mainly determined by
precomputed proposals, thereby being limited in precise object localization. In
this paper, we defend the problem setting for improving localization
performance by leveraging the bounding box regression knowledge from a
well-annotated auxiliary dataset. First, we use the well-annotated auxiliary
dataset to explore a series of learnable bounding box adjusters (LBBAs) in a
multi-stage training manner, which is class-agnostic. Then, only LBBAs and a
weakly-annotated dataset with non-overlapped classes are used for training
LBBA-boosted WSOD. As such, our LBBAs are practically more convenient and
economical to implement while avoiding the leakage of the auxiliary
well-annotated dataset. In particular, we formulate learning bounding box
adjusters as a bi-level optimization problem and suggest an EM-like multi-stage
training algorithm. Then, a multi-stage scheme is further presented for
LBBA-boosted WSOD. Additionally, a masking strategy is adopted to improve
proposal classification. Experimental results verify the effectiveness of our
method. Our method performs favorably against state-of-the-art WSOD methods and
knowledge transfer model with similar problem setting. Code is publicly
available at \url{https://github.com/DongSky/lbba_boosted_wsod}.
