Experimental Design Using Interlacing Polynomials
This work offers a deterministic framework for experimental design, potentially benefiting researchers in statistics and optimization, though it appears incremental as it builds on existing methods.
The authors tackled experimental design problems by developing a unified deterministic approach using interlacing polynomials, which recovered best-known approximation guarantees for D/A/E-design problems and provided improved guarantees for E-design in small budget regimes.
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.