Experimental Design Using Interlacing Polynomials

TL;DR

This paper introduces a deterministic framework using interlacing polynomials for experimental design, achieving optimal guarantees and improvements in challenging regimes for D/A/E-design problems.

Contribution

It provides a unified approach that simplifies analysis and improves approximation guarantees for various experimental design problems.

Findings

Recovers best-known guarantees for D/A/E-designs

Provides improved guarantees for E-design in small budgets

Achieves optimal approximation for a generalized ratio objective

Abstract

We present a unified deterministic approach for experimental design problems using the method of interlacing polynomials. Our framework recovers the best-known approximation guarantees for the well-studied D/A/E-design problems with simple analysis. Furthermore, we obtain improved non-trivial approximation guarantee for E-design in the challenging small budget regime. Additionally, our approach provides an optimal approximation guarantee for a generalized ratio objective that generalizes both D-design and A-design.