  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 learning
approach to estimate the Pareto front by maximizing the dominated hypervolume
(HV) of the average loss vectors corresponding to a set of learners, leveraging
established multi-objective optimization methods. In our approach, the set of
learners are trained multi-objectively with a dynamic loss function, wherein
each learner's losses are weighted by their HV maximizing gradients.
Consequently, the learners get trained according to different trade-offs on the
Pareto front, which otherwise is not guaranteed for fixed linear scalarizations
or when optimizing for specific trade-offs per learner without knowing the
shape of the Pareto front. Experiments on three different multi-objective tasks
show that the outputs of the set of learners are indeed well-spread on the
Pareto front. Further, the outputs corresponding to validation samples are also
found to closely follow the trade-offs that were learned from training samples
for our set of benchmark problems.
