A column generation approach to exact experimental design

TL;DR

This paper introduces a column generation method for solving the exact D-optimal experimental design problem efficiently, especially for large-scale instances, by rapidly identifying the support of its relaxation.

Contribution

It proposes a novel column generation framework combined with semidefinite programming to improve computational speed and solution quality over existing methods.

Findings

Achieves faster solutions for large-scale experimental design problems.

Provides solutions close to the optimal with high reliability.

Outperforms branch-and-bound algorithms in efficiency and quality.

Abstract

In this work, we address the exact D-optimal experimental design problem by proposing an efficient algorithm that rapidly identifies the support of its continuous relaxation. Our method leverages a column generation framework to solve such a continuous relaxation, where each restricted master problem is tackled using a Primal-Dual Interior-Point-based Semidefinite Programming solver. This enables fast and reliable detection of the design's support. The identified support is subsequently used to construct a feasible exact design that is provably close to optimal. We show that, for large-scale instances in which the number of regression points exceeds by far the number of experiments, our approach achieves superior performance compared to existing branch-and-bound-based algorithms in both computational efficiency and solution quality.