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One-stage object detectors are trained by optimizing classification-loss and localization-loss simultaneously, with the former suffering much from extreme foreground-background class imbalance issue due to the large number of anchors. This paper alleviates this issue by proposing a novel framework to replace the classification task in one-stage detectors with a ranking task, and adopting the Average-Precision loss (AP-loss) for the ranking problem. Due to its non-differentiability and non-convexity, the AP-loss cannot be optimized directly. For this purpose, we develop a novel optimization algorithm, which seamlessly combines the error-driven update scheme in perceptron learning and backpropagation algorithm in deep networks. We provide in-depth analyses on the good convergence property and computational complexity of the proposed algorithm, both theoretically and empirically. Experimental results demonstrate notable improvement in addressing the imbalance issue in object detection over existing AP-based optimization algorithms. An improved state-of-the-art performance is achieved in one-stage detectors based on AP-loss over detectors using classification-losses on various standard benchmarks. The proposed framework is also highly versatile in accommodating different network architectures. Code is available at https://github.com/cccorn/AP-loss .