A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments

Radoslav Harman; Lenka Filová; Peter Richtárik

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arXiv · 1801.05661

A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments

Radoslav Harman·Lenka Filová·Peter Richtárik

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Abstract

We propose a class of subspace ascent methods for computing optimal approximate designs that covers both existing as well as new and more efficient algorithms. Within this class of methods, we construct a simple, randomized exchange algorithm (REX). Numerical comparisons suggest that the performance of REX is comparable or superior to the performance of state-of-the-art methods across a broad range of problem structures and sizes. We focus on the most commonly used criterion of D-optimality that also has applications beyond experimental design, such as the construction of the minimum volume ellipsoid containing a given set of data-points. For D-optimality, we prove that the proposed algorithm converges to the optimum. We also provide formulas for the optimal exchange of weights in the case of the criterion of A-optimality. These formulas enable one to use REX for computing A-optimal and I-optimal designs.

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BibTeX RIS

Radoslav Harman, Lenka Filová, Peter Richtárik. 2018-01-17. A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments. https://arxiv.org/abs/1801.05661

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