Computing Optimal Experimental Designs via Interior Point Method

TL;DR

This paper introduces an interior point method for solving a broad class of convex optimal experimental design problems, demonstrating improved efficiency and solution quality over existing algorithms through theoretical analysis and computational experiments.

Contribution

The paper develops a new interior point algorithm for convex optimal experimental design problems, providing convergence guarantees and efficient computation techniques.

Findings

IP method outperforms multiplicative algorithm in speed

IP method achieves higher solution quality

Explicit Hessian rank formula enables efficient Newton direction computation

Abstract

In this paper, we study optimal experimental design problems with a broad class of smooth convex optimality criteria, including the classical A-, D- and p th mean criterion. In particular, we propose an interior point (IP) method for them and establish its global convergence. Furthermore, by exploiting the structure of the Hessian matrix of the aforementioned optimality criteria, we derive an explicit formula for computing its rank. Using this result, we then show that the Newton direction arising in the IP method can be computed efficiently via Sherman-Morrison-Woodbury formula when the size of the moment matrix is small relative to the sample size. Finally, we compare our IP method with the widely used multiplicative algorithm introduced by Silvey et al. [29]. The computational results show that the IP method generally outperforms the multiplicative algorithm both in speed and solution quality.