A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments

TL;DR

This paper introduces a randomized exchange algorithm (REX) for efficiently computing optimal approximate experimental designs, demonstrating superior performance and convergence guarantees for D-optimality and extensions to A- and I-optimality.

Contribution

The paper develops a new randomized exchange algorithm (REX) that unifies and improves upon existing methods for optimal design computation, with proven convergence for D-optimality.

Findings

REX performs comparably or better than state-of-the-art algorithms.

REX converges to the optimal design for D-optimality.

Formulas for optimal weight exchange enable extensions to A- and I-optimality.

Abstract

We propose a class of subspace ascent methods for computing optimal approximate designs that covers both existing as well as new and more efficient algorithms. Within this class of methods, we construct a simple, randomized exchange algorithm (REX). Numerical comparisons suggest that the performance of REX is comparable or superior to the performance of state-of-the-art methods across a broad range of problem structures and sizes. We focus on the most commonly used criterion of D-optimality that also has applications beyond experimental design, such as the construction of the minimum volume ellipsoid containing a given set of data-points. For D-optimality, we prove that the proposed algorithm converges to the optimum. We also provide formulas for the optimal exchange of weights in the case of the criterion of A-optimality. These formulas enable one to use REX for computing A-optimal and I-optimal designs.