In decision-making problem under uncertainty, predicting unknown parameters is often considered independent of the optimization part. Decision-focused Learning (DFL) is a task-oriented framework to integrate prediction and optimization by adapting predictive model to give better decision for the corresponding task. Here, an inevitable challenge arises when computing gradients of the optimal decision with respect to the parameters. Existing researches cope this issue by smoothly reforming surrogate optimization or construct surrogate loss function that mimic task loss. However, they are applied to restricted optimization domain. In this paper, we propose Locally Convex Global Loss Network (LCGLN), a global surrogate loss model which can be implemented in a general DFL paradigm. LCGLN learns task loss via 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 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（DFL）是一种面向任务的框架，通过调整预测模型以针对相应任务提供更优决策，从而整合预测与优化。在此过程中，计算最优决策相对于参数的梯度时，一个不可避免的挑战随之出现。现有研究通过平滑重构替代优化或构建模仿任务损失的替代损失函数来处理此问题。然而，这些方法仅适用于受限的优化领域。本文提出局部凸全局损失网络（LCGLN），这是一种可在通用DFL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是凸的，同时保持对其他输入的非凸全局结构。这使得LCGLN能够仅通过单一替代损失实现通用DFL，而无需考虑选择适当的参数形式。我们通过三个随机决策问题评估所提出的模型，验证了LCGLN的有效性和灵活性。