Data-driven robust optimization in the face of large-scale datasets: An incremental learning approach

One of the most significant current discussions in optimization under deep uncertainty is integrating machine learning and data science into robust optimization, which has led to the emergence of a new field called Data-Driven Robust Optimization (DDRO). When creating data-driven uncertainty sets, it considers a dataset’s complexity, hidden information, and inherent form. One of the more practical machine learning algorithms for creating data-driven uncertainty sets is support vector clustering (SVC). This algorithm has no prerequisites for preliminary information to generate uncertainty sets with arbitrary geometry. More scenarios can reduce risk when developing SVC-based uncertainty sets. However, the lack of a systematic way to manage the large number of these scenarios hinders the employment of SVC. This paper puts forward an incremental learning algorithm based on support vector clustering, called Incremental Support Vector Clustering (ISVC), to construct an uncertainty set incrementally and efficiently using large datasets. This approach’s novelty and main contributions include incrementally constructing uncertainty sets and dynamic management of outliers. In order to update the temporarily stored Bounded Support Vectors (BSV) and identify outliers, the idea of BSV-archive is offered, where the revision-and-recycle operation is tailored to do just that. As a result, some of the newly acquired information is preserved. Experiments on large-scale datasets demonstrate that the proposed ISVC approach can create an uncertainty set comparable to that of an SVC-based method while using significantly less time.