Decision-Driven Regularization: Harmonizing the Predictive and Prescriptive
Decision-Driven Regularization: Harmonizing the Predictive and Prescriptive
复制标题
决策驱动的正则化：协调预测性和规范性
DOI：
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复制
发表时间：
2020
期刊：
影响因子：
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通讯作者：
Yangge Xiao
中科院分区：
文献类型：
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作者：
G. Loke;Qinshen Tang;Yangge Xiao
联合预测和优化问题在许多业务应用中很常见，从客户关系管理和营销到收入和零售运营管理。这些问题涉及第一阶段的学习模型（根据特征预测结果）和第二阶段的决策过程（根据这些结果选择最佳决策）。在实践中，这两个阶段是分开进行的，但不是最佳的。在这项工作中，我们提出了一种新颖的模型，可以将两个部分作为一个整体来解决，但在许多情况下在计算上是易于处理的。具体来说，我们引入了正则化器的概念，它根据决策过程中产生的成本来衡量预测模型的价值。我们将这种决策驱动的正则化称为决策驱动的正则化，它的前提是学习问题中的偏差-方差权衡不会被后续决策问题线性变换。此外，这也解释了我们确定的成本函数定义的模糊性。我们证明了模型的关键属性，即它是一致的、对错误估计具有鲁棒性并且具有有限偏差。我们还研究了特殊情况，在这些情况下，我们与文献中的现有模型建立了联系，提出了混合模型，并能够使用我们的框架作为理论基础来描述其有效性。在我们的数值实验中，我们说明了我们模型的行为，以及它相对于文献中其他模型的性能。
Joint prediction and optimization problems are common in many business applications ranging from customer relationship management and marketing to revenue and retail operations management. These problems involve a first-stage learning model, where outcomes are predicted from features, and a second-stage decision process, which selects the optimal decisions based on these outcomes. In practice, these two stages are conducted separately, but is sub-optimal. In this work, we propose a novel model that solves both parts as a whole, but is computationally tractable under many circumstances. Specifically, we introduce the notion of a regularizer that measures the value of a predictive model in terms of the cost incurred in the decision process. We term this decision-driven regularization, and it is centred on the premise that the bias-variance trade-off in the learning problem is not transformed linearly by the subsequent decision problem. Additionally, this accounts for the ambiguity in the definition of the cost function, which we identify. We prove key properties of our model, namely, that it is consistent, robust to wrong estimation, and has bounded bias. We also examine special cases under which we draw links to existing models in the literature, propose hybrid models and are able to describe their effectiveness using our framework as a theoretical basis. In our numerical experiments, we illustrate the behaviour of our model, and its performance against other models in the literature.
影响因子：
1
作者：
Blanchet, Jose;Kang, Yang;Murthy, Karthyek
通讯作者：
Murthy, Karthyek
DOI：
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发表时间：
2020
期刊：
Proceedings of the 37th International Conference on Machine Learning
影响因子：
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作者：
Elmachtoub, Adam N;Liang, Jason C;McNellis, Ryan
通讯作者：
McNellis, Ryan