Optimal experimental design via gradient flow

Optimal experimental design (OED) has far-reaching impacts in many scientific domains. We study OED over a continuous-valued design space, a setting that occurs often in practice. Optimization of a distributional function over an infinite-dimensional probability measure space is conceptually distinct from the discrete OED tasks that are conventionally tackled. We propose techniques based on optimal transport and Wasserstein gradient flow. A practical computational approach is derived from the Monte Carlo simulation, which transforms the infinite-dimensional optimization problem to a finite-dimensional problem over Euclidean space, to which gradient descent can be applied. We discuss first-order criticality and study the convexity properties of the OED objective. We apply our algorithm to the tomography inverse problem, where the solution reveals optimal sensor placements for imaging.