Optimising a ranking-based metric, such as Average Precision (AP), is notoriously challenging due to the fact that it is non-differentiable, and hence cannot be optimised directly using gradient-descent methods. To this end, we introduce an objective that optimises instead a smoothed approximation of AP, coined Smooth-AP. Smooth-AP is a plug-and-play objective function that allows for end-to-end training of deep networks with a simple and elegant implementation. We also present an analysis for why directly optimising the ranking based metric of AP offers benefits over other deep metric learning losses. We apply Smooth-AP to standard retrieval benchmarks: Stanford Online products and VehicleID, and also evaluate on larger-scale datasets: INaturalist for fine-grained category retrieval, and VGGFace2 and IJB-C for face retrieval. In all cases, we improve the performance over the state-of-the-art, especially for larger-scale datasets, thus demonstrating the effectiveness and scalability of Smooth-AP to real-world scenarios.

介绍了 Smooth-AP 的目标函数来近似优化平均精度；这次研究对标准的检索基准、大规模的数据集进行评估，优于现有技术并展示了 Smooth-AP 在真实场景中的有效性和可扩展性。

Smooth-AP：平滑大规模图像检索路径