ﻻ يوجد ملخص باللغة العربية
The predict-then-optimize framework is fundamental in practical stochastic decision-making problems: first predict unknown parameters of an optimization model, then solve the problem using the predicted values. A natural loss function in this setting is defined by measuring the decision error induced by the predicted parameters, which was named the Smart Predict-then-Optimize (SPO) loss by Elmachtoub and Grigas [arXiv:1710.08005]. Since the SPO loss is typically nonconvex and possibly discontinuous, Elmachtoub and Grigas [arXiv:1710.08005] introduced a convex surrogate, called the SPO+ loss, that importantly accounts for the underlying structure of the optimization model. In this paper, we greatly expand upon the consistency results for the SPO+ loss provided by Elmachtoub and Grigas [arXiv:1710.08005]. We develop risk bounds and uniform calibration results for the SPO+ loss relative to the SPO loss, which provide a quantitative way to transfer the excess surrogate risk to excess true risk. By combining our risk bounds with generalization bounds, we show that the empirical minimizer of the SPO+ loss achieves low excess true risk with high probability. We first demonstrate these results in the case when the feasible region of the underlying optimization problem is a polyhedron, and then we show that the results can be strengthened substantially when the feasible region is a level set of a strongly convex function. We perform experiments to empirically demonstrate the strength of the SPO+ surrogate, as compared to standard $ell_1$ and squared $ell_2$ prediction error losses, on portfolio allocation and cost-sensitive multi-class classification problems.
Many real-world analytics problems involve two significant challenges: prediction and optimization. Due to the typically complex nature of each challenge, the standard paradigm is predict-then-optimize. By and large, machine learning tools are intend
The predict-then-optimize framework is fundamental in many practical settings: predict the unknown parameters of an optimization problem, and then solve the problem using the predicted values of the parameters. A natural loss function in this environ
Combinatorial optimization assumes that all parameters of the optimization problem, e.g. the weights in the objective function is fixed. Often, these weights are mere estimates and increasingly machine learning techniques are used to for their estima
In the predict-then-optimize framework, the objective is to train a predictive model, mapping from environment features to parameters of an optimization problem, which maximizes decision quality when the optimization is subsequently solved. Recent wo
A desirable property of learning systems is to be both effective and interpretable. Towards this goal, recent models have been proposed that first generate an extractive explanation from the input text and then generate a prediction on just the expla