Many real-world optimization problems contain unknown parameters that must be predicted prior to solving. To train the predictive machine learning (ML) models involved, the commonly adopted approach focuses on maximizing predictive accuracy. However, this approach does not always lead to the minimization of the downstream task loss. Decision-focused learning (DFL) is a recently proposed paradigm whose goal is to train the ML model by directly minimizing the task loss. However, state-of-the-art DFL methods are limited by the assumptions they make about the structure of the optimization problem (e.g., that the problem is linear) and by the fact that can only predict parameters that appear in the objective function. In this work, we address these limitations by instead predicting \textit{distributions} over parameters and adopting score function gradient estimation (SFGE) to compute decision-focused updates to the predictive model, thereby widening the applicability of DFL. Our experiments show that by using SFGE we can: (1) deal with predictions that occur both in the objective function and in the constraints; and (2) effectively tackle two-stage stochastic optimization problems.

翻译：许多现实世界的优化问题包含必须在求解前进行预测的未知参数。为训练所涉及的预测性机器学习模型，通常采用的方法侧重于最大化预测精度。然而，这种方法并不总能导致下游任务损失的最小化。决策导向学习（DFL）是最近提出的一种范式，其目标是通过直接最小化任务损失来训练机器学习模型。然而，最先进的DFL方法受到其对优化问题结构假设（例如问题为线性）以及仅能预测出现在目标函数中的参数这两方面的限制。在本工作中，我们通过预测参数上的分布并采用评分函数梯度估计（SFGE）来计算预测模型的决策导向更新，从而解决了这些限制，进而扩展了DFL的适用范围。我们的实验表明，通过使用SFGE，我们能够：（1）处理同时出现在目标函数和约束中的预测；（2）有效应对两阶段随机优化问题。