  Multi-objective optimization (MOO) problems are prevalent in machine
learning. These problems have a set of optimal solutions, called the Pareto
front, where each point on the front represents a different trade-off between
possibly conflicting objectives. Recent MOO methods can target a specific
desired ray in loss space however, most approaches still face two grave
limitations: (i) A separate model has to be trained for each point on the
front; and (ii) The exact trade-off must be known before the optimization
process. Here, we tackle the problem of learning the entire Pareto front, with
the capability of selecting a desired operating point on the front after
training. We call this new setup Pareto-Front Learning (PFL).
  We describe an approach to PFL implemented using HyperNetworks, which we term
Pareto HyperNetworks (PHNs). PHN learns the entire Pareto front simultaneously
using a single hypernetwork, which receives as input a desired preference
vector and returns a Pareto-optimal model whose loss vector is in the desired
ray. The unified model is runtime efficient compared to training multiple
models and generalizes to new operating points not used during training. We
evaluate our method on a wide set of problems, from multi-task regression and
classification to fairness. PHNs learn the entire Pareto front at roughly the
same time as learning a single point on the front and at the same time reach a
better solution set. Furthermore, we show that PHNs can scale to generate large
models like ResNet18. PFL opens the door to new applications where models are
selected based on preferences that are only available at run time.
