以数据增强方式实现鲁棒的数据驱动情境决策
Achieving Robust Data-driven Contextual Decision Making in a Data Augmentation Way
AI总结：
本文针对基于Wasserstein距离的分布鲁棒情境优化问题，提出一种基于数据增强的随机梯度下降算法，能以O(1/√T)速率收敛并适用于在线场景，实验表明其性能优于多个基准方法。
摘要：
本文关注情境优化问题，其中决策受到某些不确定参数的影响，并且在做出决策之前可以获得对这些参数具有一定预测能力的协变量。更具体地说，我们重点求解该问题基于Wasserstein距离的分布鲁棒优化（DRO）模型，该模型在一个包含所有与名义分布在Wasserstein距离意义下足够接近的分布的不确定集合上最大化最坏情况期望目标。我们基于数据增强思想开发了一种随机梯度下降算法以高效求解该模型。该算法迭代地：a）从名义分布中进行自助采样；b）对样本进行对抗性扰动；c）更新决策。相应地，该算法的计算时间仅由迭代次数和计算单样本梯度的复杂度决定。除了高效求解模型之外，该算法还提供了额外的优势，即所提算法能够处理任意名义分布，因此可扩展到在线场景中求解该问题。我们还证明了该算法以$O(1/\sqrt{T})$的速率收敛到DRO模型的最优解，其中$T$是自助采样的迭代次数。因此，该算法的性能保证为DRO模型的性能保证加上$O(1/\sqrt{T})$。通过大量数值实验，我们证明了所提算法相对于若干基准方法的优越性能。
英文摘要：
This paper focuses on the contextual optimization problem where a decision is subject to some uncertain parameters and covariates that have some predictive power on those parameters are available before the decision is made. More specifically, we focus on solving the Wasserstein-distance-based distributionally robust optimization (DRO) model for the problem, which maximizes the worst-case expected objective over an uncertainty set including all distributions closed enough to a nominal distribution with respect to the Wasserstein distance. We develop a stochastic gradient descent algorithm based on the idea of data augmentation to solve the model efficiently. The algorithm iteratively a) does a bootstrapping sample from the nominal distribution; b) perturbs the adversarially and c) updates decisions. Accordingly, the computational time of the algorithm is only determined by the number of iterations and the complexity of computing the gradient of a single sample. Except for efficiently solving the model, the algorithm provide additional advantages that the proposed algorithm can cope with any nominal distributions and therefore is extendable to solve the problem in an online setting. We also prove that the algorithm converges to the optimal solution of the DRO model at a rate of a $O(1/\sqrt{T})$, where $T$ is the number of iterations of bootstrapping. Consequently, the performance guarantee of the algorithm is that of the DRO model plus $O(1/\sqrt{T})$. Through extensive numerical experiments, we demonstrate the superior performance of the proposed algorithm to several benchmarks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
