Experimental Design for Any $p$-Norm
This work addresses a foundational problem in experimental design for researchers in statistics and optimization, offering a unified algorithmic solution that is incremental in extending existing methods to a broader framework.
The paper tackles the problem of experimental design under a general p-norm objective, which includes several well-studied design criteria as special cases, and presents a randomized local search algorithm that provides the first approximation algorithm for this general objective, achieving bounds that interpolate known results for the special cases.
We consider a general $p$-norm objective for experimental design problems that captures some well-studied objectives (D/A/E-design) as special cases. We prove that a randomized local search approach provides a unified algorithm to solve this problem for all $p$. This provides the first approximation algorithm for the general $p$-norm objective, and a nice interpolation of the best known bounds of the special cases.