A global optimum-informed greedy algorithm for A-optimal experimental design

TL;DR

This paper introduces a framework to improve greedy algorithms for optimal experimental design by leveraging global optimality insights, leading to better sensor placement strategies.

Contribution

It presents a novel framework that rejects sub-optimal greedy indices in experimental design, enhancing the effectiveness of greedy algorithms.

Findings

Framework effectively identifies and rejects sub-optimal greedy choices

Numerical experiments show improved sensor placement outcomes

Method leverages recent advances in non-smooth convex optimization

Abstract

Optimal experimental design (OED) concerns itself with identifying ideal methods of data collection, e.g.~via sensor placement. The \emph{greedy algorithm}, that is, placing one sensor at a time, in an iteratively optimal manner, stands as an extremely robust and easily executed algorithm for this purpose. However, it is a priori unclear whether this algorithm leads to sub-optimal regimes. Taking advantage of the author's recent work on non-smooth convex optimality criteria for OED, we here present a framework for rejection of sub-optimal greedy indices, and study the numerical benefits this offers.