A Local Search Framework for Experimental Design

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