Adaptive discretization algorithms for locally optimal experimental design

TL;DR

This paper introduces adaptive discretization algorithms for nonlinear experimental design, providing theoretical convergence guarantees and demonstrating practical effectiveness through chemical engineering applications.

Contribution

It presents novel adaptive algorithms with proven convergence rates and finite termination guarantees for nonlinear experimental design problems.

Findings

Proven sublinear convergence rate under general conditions.

Linear convergence under strong convexity and finite design space.

Finite termination with bounds on iterations.

Abstract

We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish novel termination, convergence, and convergence rate results for the proposed algorithms. In particular, we prove a sublinear convergence rate result under very general assumptions on the design criterion and, most notably, a linear convergence result under the additional assumption that the design criterion is strongly convex and the design space is finite. Additionally, we prove the finite termination at approximately optimal designs, including upper bounds on the number of iterations until termination. And finally, we illustrate the practical use of the proposed algorithms by means of two application examples from chemical engineering: one with a stationary model and one with a dynamic model.