A Local Search Framework for Experimental Design

TL;DR

This paper introduces a versatile local search framework for designing and analyzing algorithms in experimental design, unifying existing methods and enabling new results across combinatorial and rounding algorithms with broader applications.

Contribution

It provides a unified local search approach that improves analysis and design of algorithms for D/A/E-design, including new algorithms and extensions to complex constraints.

Findings

Improved analysis of Fedorov's exchange method.

New local search algorithm for E-design using regret minimization.

Algorithm applicable to multiple knapsack constraints and fairness considerations.

Abstract

We present a local search framework to design and analyze both combinatorial algorithms and rounding algorithms for experimental design problems. This framework provides a unifying approach to match and improve all known results in D/A/E-design and to obtain new results in previously unknown settings. For combinatorial algorithms, we provide a new analysis of the classical Fedorov's exchange method. We prove that this simple local search algorithm works well as long as there exists an almost optimal solution with good condition number. Moreover, we design a new combinatorial local search algorithm for E-design using the regret minimization framework. For rounding algorithms, we provide a unified randomized exchange algorithm to match and improve previous results for D/A/E-design. Furthermore, the algorithm works in the more general setting to approximately satisfy multiple knapsack constraints, which can be used for weighted experimental design and for incorporating fairness constraints into experimental design.