Abstract Robust optimization (RO) has been broadly utilized for decision-making under uncertainty; however, as a key issue in RO the design of the uncertainty set could exert significant influence on both the conservatism of solutions and tractability of induced problems. In this paper, we propose a novel multiple kernel learning (MKL)-aided RO framework for data-driven decision-making, by developing an efficient approach for uncertainty set construction from data based on one-class support vector machine. The learnt polyhedral uncertainty set not only achieves a compact encircling of empirical data, which alleviates the pessimism and reduces the gap between the model and real-world performance, but also ensures structural sparsity and computational tractability. The data-driven RO framework enables a handy adjustment of the conservatism and complexity by simply manipulating two hyper-parameters, thereby being user-friendly in practice. In addition, the proposed framework applies to adjustable RO (ARO) with the extended affine decision rule adopted, which helps improving the optimization performance without too much additional effort. Numerical and application case studies demonstrate the effectiveness of the proposed data-driven RO framework.

中文翻译：

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多核学习辅助鲁棒优化：学习算法、计算可处理性和多阶段决策中的使用

摘要 鲁棒优化（RO）已被广泛用于不确定性下的决策；然而，作为 RO 中的一个关键问题，不确定性集的设计可能会对解决方案的保守性和诱发问题的易处理性产生重大影响。在本文中，我们通过开发一种基于一类支持向量机的数据构建不确定性集的有效方法，提出了一种用于数据驱动决策的新型多核学习 (MKL) 辅助 RO 框架。学习到的多面体不确定性集不仅实现了经验数据的紧凑环绕，缓解了悲观情绪，减少了模型与现实世界性能之间的差距，而且还确保了结构稀疏性和计算易处理性。数据驱动的 RO 框架可以通过简单地操作两个超参数来方便地调整保守性和复杂性，从而在实践中对用户友好。此外，所提出的框架适用于采用扩展仿射决策规则的可调 RO（ARO），这有助于提高优化性能而无需太多额外努力。数值和应用案例研究证明了所提出的数据驱动 RO 框架的有效性。