In this short technical note we propose a baseline for decision-aware learning for contextual linear optimization, which solves stochastic linear optimization when cost coefficients can be predicted based on context information. We propose a decision-aware version of predict-then-optimize. We reweigh the prediction error by the decision regret incurred by an (unweighted) pilot estimator of costs to obtain a decision-aware predictor, then optimize with cost predictions from the decision-aware predictor. This method can be motivated as a finite-difference, iterate-independent approximation of the gradients of previously proposed end-to-end learning algorithms; it is also consistent with previously suggested intuition for end-to-end learning. This baseline is computationally easy to implement with readily available reweighted prediction oracles and linear optimization, and can be implemented with convex optimization so long as the prediction error minimization is convex. Empirically, we demonstrate that this approach can lead to improvements over a "predict-then-optimize" framework for settings with misspecified models, and is competitive with other end-to-end approaches. Therefore, due to its simplicity and ease of use, we suggest it as a simple baseline for end-to-end and decision-aware learning.
翻译:在这份简短的技术说明中,我们提议了一个基准,用于在根据背景信息预测成本系数时进行决策意识学习,从而解决在根据背景信息预测成本系数时的随机性线性优化;我们提议了一个预测-当时最佳化的决策意识版本;我们用一个(未加权的)试点估算器为获得决策意识预测器而引发的决定遗憾重新权衡了预测错误,然后用决定意识预测器的成本预测器进行优化。这种方法可以作为一种有限的差异,即对先前提议的端对端学习算法的梯度进行反复和独立的近似;我们还提出一个符合先前建议的端对端学习直觉的预测-当时最佳化版本;我们用现成的(未加权的)预测或触角和线性优化来进行计算,并且只要预测错误最小化的错误最小化,就可以以峰值优化的方式加以实施。我们很生动地证明,这一方法可以导致在错误确定模型的设置中“预测-当时-最佳化”的梯度框架的改进,它也符合先前建议的端对端到端学习算法;这一基线在计算上比较容易执行,并且具有竞争性地使用其他端到最后学习的简单和最终学习的方法。