  Cascade ranking is widely used for large-scale top-k selection problems in
online advertising and recommendation systems, and learning-to-rank is an
important way to optimize the models in cascade ranking. Previous works on
learning-to-rank usually focus on letting the model learn the complete order or
top-k order, and adopt the corresponding rank metrics (e.g. OPA and NDCG@k) as
optimization targets. However, these targets can not adapt to various cascade
ranking scenarios with varying data complexities and model capabilities; and
the existing metric-driven methods such as the Lambda framework can only
optimize a rough upper bound of limited metrics, potentially resulting in
sub-optimal and performance misalignment. To address these issues, we propose a
novel perspective on optimizing cascade ranking systems by highlighting the
adaptability of optimization targets to data complexities and model
capabilities. Concretely, we employ multi-task learning to adaptively combine
the optimization of relaxed and full targets, which refers to metrics
Recall@m@k and OPA respectively. We also introduce permutation matrix to
represent the rank metrics and employ differentiable sorting techniques to
relax hard permutation matrix with controllable approximate error bound. This
enables us to optimize both the relaxed and full targets directly and more
appropriately. We named this method as Adaptive Neural Ranking Framework
(abbreviated as ARF). Furthermore, we give a specific practice under ARF. We
use the NeuralSort to obtain the relaxed permutation matrix and draw on the
variant of the uncertainty weight method in multi-task learning to optimize the
proposed losses jointly. Experiments on a total of 4 public and industrial
benchmarks show the effectiveness and generalization of our method, and online
experiment shows that our method has significant application value.
