Computing optimal experimental designs on finite sets by log-determinant gradient flow

TL;DR

This paper introduces a new algorithm for computing optimal experimental designs on finite sets using the gradient flow of the log-determinant of the information matrix, with proven convergence and practical implementation.

Contribution

It presents a novel gradient flow-based algorithm for optimal design computation on finite sets, including convergence proof and rate estimates.

Findings

Algorithm converges to optimal designs.

Provides a sharp estimate on convergence rate.

Demonstrates effectiveness through numerical experiments.

Abstract

Optimal experimental designs are probability measures with finite support enjoying an optimality property for the computation of least squares estimators. We present an algorithm for computing optimal designs on finite sets based on the long-time asymptotics of the gradient flow of the log-determinant of the so called information matrix. We prove the convergence of the proposed algorithm, and provide a sharp estimate on the rate its convergence. Numerical experiments are performed on few test cases using the new matlab package OptimalDesignComputation.