Multi-Objective Learning to Predict Pareto Fronts Using Hypervolume Maximization
This work provides a method for machine learning practitioners to generate diverse, optimal trade-off predictions for multi-objective problems, especially when preferences are unknown or complex. It offers an incremental improvement over existing methods for approximating Pareto fronts.
This paper addresses the challenge of predicting multiple optimal trade-offs in multi-objective problems without prior specification of preferences. The authors propose a novel multi-objective training approach for neural networks that uses a dynamic loss function weighted by hypervolume maximizing gradients, enabling the networks to approximate the Pareto front during inference. Experiments on three multi-objective problems demonstrate that the approach produces well-spread outputs across different trade-offs on the approximated Pareto front, outperforming state-of-the-art methods, particularly for asymmetric Pareto fronts.
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.