Learning with non-modular losses is an important problem when sets of predictions are made simultaneously. The main tools for constructing convex surrogate loss functions for set prediction are margin rescaling and slack rescaling. In this work, we show that these strategies lead to tight convex surrogates if the underlying loss function is increasing in the number of incorrect predictions. However, gradient or cutting-plane computation for these functions is NP-hard for non-supermodular loss functions. We propose instead a novel surrogate loss function for submodular losses, the Lovasz hinge, which leads to O(p log p) complexity with O(p) oracle accesses to the loss function to compute a gradient or cutting-plane. We prove that the Lovasz hinge is convex and yields an extension. As a result, we have developed the first tractable convex surrogates in the literature for submodular losses. We demonstrate the utility of this novel convex surrogate through several set prediction tasks, including on the PASCAL VOC and Microsoft COCO datasets.

中文翻译：

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Lov谩sz 铰链：子模损失的新型凸替代物


当同时进行多组预测时，非模损失学习是一个重要问题。构建用于集合预测的凸代理损失函数的主要工具是边际重新缩放和松弛重新缩放。在这项工作中，我们表明，如果潜在损失函数的错误预测数量增加，这些策略会导致紧凸代理。然而，这些函数的梯度或剖切面计算对于非超模损失函数来说是 NP 困难的。相反，我们提出了一种新的子模损失替代损失函数，即 Lovasz 铰链，它会导致 O(p log p) 复杂性，并且 O(p) 预言机访问损失函数来计算梯度或切割平面。我们证明洛瓦斯铰链是凸的并且产生延伸。因此，我们在文献中开发了第一个用于子模损失的易于处理的凸代理。我们通过几组预测任务（包括 PASCAL VOC 和 Microsoft COCO 数据集）展示了这种新颖的凸代理的实用性。