Submodularity and Randomized rounding techniques for Optimal Experimental Design

We review recent results obtained by the authors on the approximability of a family of combinatorial problems arising in optimal experimental design. We first recall a result based on submodularity, which states that the greedy approach always gives a design within 1 − 1/e of the optimal solution. Then, we present a new result on the design found by rounding the solution of the continuous relaxed problem, an approach which has been applied by several authors: When the goal is to select n out of s experiments, the D−optimal design may be rounded to a design for which the dimension of the observable subspace is within ns of the optimum.