The Limits of Experimental Design: Covariate Balance Beyond Low Dimension

What the math gives to ML

The paper gives a direct identity linking estimator variance to the squared imbalance of a covariate-dependent outcome function under signed assignments. Its transferable asset is discrepancy minimization as a principled way to construct low-variance finite-sample averages over a restricted function class, together with an explicit warning that unrestricted high-dimensional balance is impossible. A practical neural-network adaptation is to select minibatches whose learned feature statistics have low discrepancy from the candidate-pool statistics, reducing stochastic gradient noise without requiring a larger batch.