We introduce a nonlinear covariance shrinkage method for building optimal portfolios. Our universal portfolio shrinkage approximator (UPSA) is built from closed-form basis portfolios, is cheap to implement, and improves on existing shrinkage methods. Rather than uniformly penalizing all principal components of returns or discarding low-variance ones, UPSA instead reweights components to explicitly optimize expected out-of-sample portfolio performance. In empirical applications using a large cross-section of anomaly factors, it delivers robust improvements over alternative shrinkage methods in the literature.