Competitive least squares problem with bounded data uncertainties

Abstract

We study robust least squares problem with bounded data uncertainties in a competitive algorithm framework. We propose a competitive least squares (LS) approach that minimizes the worst case “regret” which is the difference between the squared data error and the smallest attainable squared data error of an LS estimator. We illustrate that the robust least squares problem can be put in an SDP form for both structured and unstructured data matrices and uncertainties. Through numerical examples we demonstrate the potential merit of the proposed approaches.