  In industry, feature selection is a standard but necessary step to search for
an optimal set of informative feature fields for efficient and effective
training of deep Click-Through Rate (CTR) models. Most previous works measure
the importance of feature fields by using their corresponding continuous
weights from the model, then remove the feature fields with small weight
values. However, removing many features that correspond to small but not exact
zero weights will inevitably hurt model performance and not be friendly to
hot-start model training. There is also no theoretical guarantee that the
magnitude of weights can represent the importance, thus possibly leading to
sub-optimal results if using these methods.
  To tackle this problem, we propose a novel Learnable Polarizing Feature
Selection (LPFS) method using a smoothed-$\ell^0$ function in literature.
Furthermore, we extend LPFS to LPFS++ by our newly designed
smoothed-$\ell^0$-liked function to select a more informative subset of
features. LPFS and LPFS++ can be used as gates inserted at the input of the
deep network to control the active and inactive state of each feature. When
training is finished, some gates are exact zero, while others are around one,
which is particularly favored by the practical hot-start training in the
industry, due to no damage to the model performance before and after removing
the features corresponding to exact-zero gates. Experiments show that our
methods outperform others by a clear margin, and have achieved great A/B test
results in KuaiShou Technology.
