We propose a novel family of decision-aware surrogate losses, called Perturbation Gradient (PG) losses, for the predict-then-optimize framework. These losses directly approximate the downstream decision loss and can be optimized using off-the-shelf gradient-based methods. Importantly, unlike existing surrogate losses, the approximation error of our PG losses vanishes as the number of samples grows. This implies that optimizing our surrogate loss yields a best-in-class policy asymptotically, even in misspecified settings. This is the first such result in misspecified settings and we provide numerical evidence confirming our PG losses substantively outperform existing proposals when the underlying model is misspecified and the noise is not centrally symmetric. Insofar as misspecification is commonplace in practice -- especially when we might prefer a simpler, more interpretable model -- PG losses offer a novel, theoretically justified, method for computationally tractable decision-aware learning.

翻译：我们提出了一类新型决策感知替代损失函数，称为扰动梯度（Perturbation Gradient, PG）损失，用于预测-优化框架。这些损失函数直接逼近下游决策损失，并可通过现成的基于梯度的优化方法进行训练。重要的是，与现有替代损失函数不同，我们的PG损失的近似误差会随样本量增加而消失。这意味着即使在模型设定错误的情况下，优化我们的替代损失函数也能渐近地得到类别最优策略。这是首个在模型设定错误情形下取得该结果的研究，我们提供的数值实验表明：当基础模型设定错误且噪声不呈中心对称分布时，PG损失显著优于现有方案。鉴于模型设定错误在实际应用中普遍存在（尤其是当我们倾向于选择更简单、更具可解释性的模型时），PG损失为可计算决策感知学习提供了一种具有理论依据的新型方法。