The accelerated discovery of materials for real world applications requires the achievement of multiple design objectives. Satisfaction of such constraints requires exploration of multi-million compound libraries over which even density-functional theory (DFT) screening is intractable. Machine learning (ML, e.g., artificial neural network, ANN, or Gaussian process, GP) models for this task are limited by training data availability and predictive uncertainty quantification (UQ). We overcome such limitations by using efficient global optimization (EGO) with the multi-dimensional expected improvement (EI) criterion. EGO balances exploitation of a trained model with acquisition of new DFT data at the Pareto front, the region of chemical space that contains the optimal trade-off between multiple design criteria. We demonstrate this approach for the simultaneous optimization of redox potential and solubility in candidate M(II)/M(III) redox couples for redox flow batteries from a space of 2.8M transition metal complexes designed for stability in practical RFB applications. We employ latent-distance-based UQ with a multi-task ANN to enable model generalization that surpasses that of a GP. With this approach, ANN prediction and EI scoring of the full 2.8M complex space is achieved in minutes. Starting from ca. 100 representative points, EGO improves both properties by 3-4 standard deviations in only five generations. Analysis of lookahead errors confirms rapid ANN model improvement during the EGO process, achieving suitable accuracy for predictive design in the space of transition metal complexes. The ANN-driven EI approach achieves at least 500-fold acceleration over random search, identifying a Pareto-optimal design in around five weeks instead of fifty years.