Multiple kernel learning-aided robust optimization: Learning algorithm, computational tractability, and usage in multi-stage decision-making

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.