Decision-focused learning (DFL) has recently emerged as a powerful approach for predict-then-optimize problems by customizing a predictive model to a downstream optimization task. However, existing end-to-end DFL methods are hindered by three significant bottlenecks: model mismatch error, sample average approximation error, and gradient approximation error. Model mismatch error stems from the misalignment between the model's parameterized predictive distribution and the true probability distribution. Sample average approximation error arises when using finite samples to approximate the expected optimization objective. Gradient approximation error occurs as DFL relies on the KKT condition for exact gradient computation, while most methods approximate the gradient for backpropagation in non-convex objectives. In this paper, we present DF2 -- the first \textit{distribution-free} decision-focused learning method explicitly designed to address these three bottlenecks. Rather than depending on a task-specific forecaster that requires precise model assumptions, our method directly learns the expected optimization function during training. To efficiently learn the function in a data-driven manner, we devise an attention-based model architecture inspired by the distribution-based parameterization of the expected objective. Our method is, to the best of our knowledge, the first to address all three bottlenecks within a single model. We evaluate DF2 on a synthetic problem, a wind power bidding problem, and a non-convex vaccine distribution problem, demonstrating the effectiveness of DF2.

翻译：决策聚焦学习（DFL）近年来已成为预测-优化问题中的一种强大方法，其通过将预测模型定制化地适配到下游优化任务中。然而，现有的端到端DFL方法受限于三个显著瓶颈：模型失配误差、样本均值近似误差和梯度近似误差。模型失配误差源于模型参数化预测分布与真实概率分布之间的不一致；样本均值近似误差源于使用有限样本近似期望优化目标；梯度近似误差则源于DFL依赖KKT条件进行精确梯度计算，而大多数方法在非凸目标中通过近似梯度实现反向传播。本文提出DF2——首个明确针对这三个瓶颈设计的**无分布假设**决策聚焦学习方法。该方法无需依赖需要精确模型假设的任务特定预测器，而是在训练过程中直接学习期望优化函数。为了以数据驱动方式高效学习该函数，我们借鉴期望目标基于分布的参数化思想，设计了一种基于注意力机制的模型架构。据我们所知，这是首个在单一模型中同时解决上述三个瓶颈的方法。我们在合成问题、风电投标问题以及非凸疫苗分配问题上评估了DF2，验证了其有效性。