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：我们提出了一种新型决策感知代理损失函数族，称为扰动梯度（PG）损失，用于预测-优化框架。这些损失直接近似下游决策损失，并可通过现成的基于梯度的优化方法进行求解。重要的是，与现有代理损失不同，我们的PG损失的近似误差会随样本量增加而趋近于零。这意味着即使存在模型误设定，优化我们的代理损失在渐近意义上也能获得最优策略。这是首个在模型误设定场景下取得该结果的成果，数值实验证实：当基础模型存在误设定且噪声非中心对称时，PG损失的实质性表现显著优于现有方法。鉴于模型误设定在实际应用中普遍存在（尤其当我们倾向于使用更简单、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方法。