无需调用优化求解器，即可高效训练预测-优化模型。
A Solver-Free Training Method for Predict-then-Optimize
- 基于测度变换原理构建无求解器的替代损失函数。
- 训练时间减少数量级，决策质量媲美顶尖方法。
- 适合大规模预测-优化任务，尤其关注训练效率的场景。
我们提出一种可扩展的方法，用于在预测-优化范式中训练预测模型，其中模型输出作为后续线性优化任务的系数。直接最小化经验决策遗憾对线性规划和组合优化而言不可行，因为决策映射是分段常数，梯度几乎处处为零。现有方法通过平滑微分过程来应对，但存在可扩展性问题，因每次梯度计算需调用昂贵的求解器。为此，我们提出基于测度变换原理的决策导向学习流程，生成一个训练期间完全无需优化求解器的替代损失函数。我们建立了理论保证，包括费雪一致性与多余风险界。实验表明，该方法在决策质量上达到与最先进方法相当的水平，同时将训练时间降低至数量级。
原文摘要 · Abstract (English)
We propose a scalable method for training prediction (machine learning) models in the predict-then-optimize paradigm, where model outputs serve as coefficients for a subsequent linear optimization task. Directly minimizing the empirical decision regret is intractable for linear programming and combinatorial optimization since the decision mapping is piecewise constant, and the gradients are zero almost everywhere. While existing methods address this by smoothing the differentiation process, they suffer from scalability issues, since a computationally expensive solver call is required for every gradient evaluation. To address this, we propose a decision-focused learning pipeline based on a measure transformation principle, which yields a new surrogate loss that is completely optimization-solver-free during training. We establish theoretical guarantees, including Fisher consistency and excess risk bounds. Empirically, our method achieves decision quality competitive with state-of-the-art methods while reducing training time by orders of magnitude.
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