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.