In decision-making problems under uncertainty, predicting unknown parameters is often considered independent of the optimization part. Decision-focused learning (DFL) is a task-oriented framework that integrates prediction and optimization by adapting the predictive model to give better decisions for the corresponding task. Here, an inevitable challenge arises when computing the gradients of the optimal decision with respect to the parameters. Existing research copes with this issue by smoothly reforming surrogate optimization or constructing surrogate loss functions that mimic task loss. However, they are applied to restricted optimization domains. In this paper, we propose Locally Convex Global Loss Network (LCGLN), a global surrogate loss model that can be implemented in a general DFL paradigm. LCGLN learns task loss via a partial input convex neural network which is guaranteed to be convex for chosen inputs while keeping the non-convex global structure for the other inputs. This enables LCGLN to admit general DFL through only a single surrogate loss without any sense for choosing appropriate parametric forms. We confirm the effectiveness and flexibility of LCGLN by evaluating our proposed model with three stochastic decision-making problems.

翻译：在不确定性下的决策问题中，未知参数的预测通常被视为独立于优化部分。决策聚焦学习是一种任务导向的框架，通过调整预测模型以针对相应任务提供更优决策，从而将预测与优化相集成。在此过程中，计算最优决策相对于参数的梯度时必然面临挑战。现有研究通过平滑重构替代优化或构建模拟任务损失的替代损失函数来应对这一问题。然而，这些方法仅适用于受限的优化域。本文提出局部凸全局损失网络，这是一种可在通用决策聚焦学习范式中实现的全局替代损失模型。LCGLN通过部分输入凸神经网络学习任务损失，该网络保证对选定输入具有凸性，同时对其他输入保持非凸的全局结构。这使得LCGLN仅需通过单一替代损失即可实现通用决策聚焦学习，无需考虑选择合适参数形式的问题。我们通过三个随机决策问题评估所提模型，验证了LCGLN的有效性和灵活性。