# A Randomized Exchange Algorithm for Optimal Design of Multi-Response Experiments

arXiv: https://arxiv.org/abs/2407.16283 · HTML: https://mlsanity.com/paper/2407.16283/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2024.

## Built on by (most cited first, 1 of 1)

- [When Is Coarse Supervision Worth It? Cost-Aware Learning under Unknown Aggregation](https://mlsanity.com/paper/2609.36704/) (2026)

## Abstract (arXiv)

Despite the increasing prevalence of vector observations, computation of optimal experimental design for multi-response models has received limited attention. To address this problem within the framework of approximate designs, we introduce mREX, an algorithm that generalizes the randomized exchange algorithm REX (J Am Stat Assoc 115:529, 2020), originally specialized for single-response models. The mREX algorithm incorporates several improvements: a novel method for computing efficient sparse initial designs, an extension to all differentiable Kiefer's optimality criteria, and an efficient method for performing optimal exchanges of weights. For the most commonly used D-optimality criterion, we propose a technique for optimal weight exchanges based on the characteristic matrix polynomial. The mREX algorithm is applicable to linear, nonlinear, and generalized linear models, and scales well to large problems. It typically converges to optimal designs faster than available alternative methods, although it does not require advanced mathematical programming solvers. We demonstrate the usefulness of mREX to bivariate dose-response Emax models for clinical trials, both without and with the inclusion of covariates.