Real-world problems are often multi-objective with decision-makers unable to specify a priori which trade-off between the conflicting objectives is preferable. Intuitively, building machine learning solutions in such cases would entail providing multiple predictions that span and uniformly cover the Pareto front of all optimal trade-off solutions. We propose a novel approach for multi-objective training of neural networks to approximate the Pareto front during inference. In our approach, the neural networks are trained multi-objectively using a dynamic loss function, wherein each network's losses (corresponding to multiple objectives) are weighted by their hypervolume maximizing gradients. We discuss and illustrate why training processes to approximate Pareto fronts need to optimize on fronts of individual training samples instead of on only the front of average losses. Experiments on three multi-objective problems show that our approach returns outputs that are well-spread across different trade-offs on the approximated Pareto front without requiring the trade-off vectors to be specified a priori. Further, results of comparisons with the state-of-the-art approaches highlight the added value of our proposed approach, especially in asymmetric Pareto fronts.
View on arXiv