发表机构
NEC Corporation（日本电气株式会社）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出超越逆优化方法，学习使最优解在各分量上优于观察行动的目标函数权重，适用于混合整数线性规划，并证明泛化误差随观察数反比下降，实验优于现有方法。
AI 中文摘要
逆优化估计目标函数的权重，这些权重将观察到的决策解释为最优解，并广泛应用于多个领域。对于混合整数线性规划（MILP），现有方法旨在将观察结果重现为最优解，因此当观察结果次优时，会学习到折衷权重。我们提出超越逆优化，其目标是寻找一组权重，使得在每个状态下，最优解在每一个分量上都优于观察到的行动。我们给出了一个损失函数，该函数仅需前向问题预言机即可评估，因此适用于MILP，并提供了基于梯度和DC优化的算法来最小化该损失。对于在所有观察点上诱导唯一超越最优解的权重，我们证明了在新状态下未能诱导出此类解的概率（即泛化误差）受限于一个与观察数量成反比的量，并且该界限在观察数量上紧致（直至对数因子）。在合成数据和真实数据的实验中，所提出的方法在预测超越行动的解决方案方面优于现有方法。
英文摘要
Inverse optimization estimates the weights of an objective function that explain observed decisions as optimal solutions, and is used in a variety of fields. For mixed-integer linear programs (MILPs), existing methods aim to reproduce the observations as optimal solutions, and thus learn compromise weights when the observations are suboptimal. We propose outperformance inverse optimization, which instead seeks weights that induce, at each state, an optimal solution outperforming the observed action in every component. We give a loss function that can be evaluated with forward-problem oracles alone and is thus applicable to MILPs, together with gradient-based and DC optimization algorithms for minimizing it. For weights inducing a unique outperforming optimal solution at all observations, we prove that the probability of failing to induce such a solution at a new state (the generalization error) is bounded by a quantity inversely proportional to the number of observations, and that this bound is tight in the number of observations up to logarithmic factors. In experiments on synthetic and real data, the proposed methods improve the prediction of solutions outperforming the actions over existing methods.
Comments81 pages
