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.

提出了一种使用动态损失函数来进行多目标训练神经网络以逼近 Pareto 前沿的新方法，在三个多目标问题上的实验表明，本方法无需预先指定权衡向量即可以返回分布在不同权衡方案上的输出，并且与现有技术相比具有更多的优势，尤其是对于非对称 Pareto 前沿。