# An Induced Natural Selection Heuristic for Finding Optimal Bayesian Experimental Designs

## TL;DR

This paper introduces a new heuristic algorithm for efficiently finding optimal Bayesian experimental designs in high-dimensional spaces, outperforming traditional methods in computational speed for problems up to 40 dimensions.

## Contribution

The authors propose a novel induced natural selection heuristic tailored for Bayesian experimental design optimization, improving computational efficiency over existing methods.

## Key findings

- The heuristic effectively evaluates designs in high-dimensional spaces.
- Compared to standard methods, it reduces computation time significantly.
- Demonstrated success on models with up to 40 dimensions.

## Abstract

Bayesian optimal experimental design has immense potential to inform the collection of data so as to subsequently enhance our understanding of a variety of processes. However, a major impediment is the difficulty in evaluating optimal designs for problems with large, or high-dimensional, design spaces. We propose an efficient search heuristic suitable for general optimisation problems, with a particular focus on optimal Bayesian experimental design problems. The heuristic evaluates the objective (utility) function at an initial, randomly generated set of input values. At each generation of the algorithm, input values are "accepted" if their corresponding objective (utility) function satisfies some acceptance criteria, and new inputs are sampled about these accepted points. We demonstrate the new algorithm by evaluating the optimal Bayesian experimental designs for the previously considered death, pharmacokinetic and logistic regression models. Comparisons to the current "gold-standard" method are given to demonstrate the proposed algorithm as a computationally-efficient alternative for moderately-large design problems (i.e., up to approximately 40-dimensions).