  Learning-to-rank has been intensively studied and has shown significantly
increasing values in a wide range of domains. The performance of
learning-to-rank methods is commonly evaluated using rank-sensitive metrics,
such as average precision (AP) and normalized discounted cumulative gain
(nDCG). Unfortunately, how to effectively optimize rank-sensitive objectives is
far from being resolved, which has been an open problem since the dawn of
learning-to-rank over a decade ago. In this paper, we introduce a simple yet
effective framework for directly optimizing information retrieval (IR) metrics.
Specifically, we propose a novel twin-sigmoid function for deriving the exact
rank positions of documents during the optimization process instead of using
approximated rank positions or relying on the traditional sorting algorithms.
Thanks to this, the rank positions are differentiable, enabling us to
reformulate the widely used IR metrics as differentiable ones and directly
optimize them based on neural networks. Furthermore, by carrying out an
in-depth analysis of the gradients, we pinpoint the potential limitations
inherent with direct optimization of IR metrics based on the vanilla sigmoid.
To break the limitations, we propose different strategies by explicitly
modifying the gradient computation. To validate the effectiveness of the
proposed framework for direct optimization of IR metrics, we conduct a series
of experiments on the widely used benchmark collection MSLRWEB30K.
