  Optimizing a set of functions simultaneously by leveraging their similarity
is called multi-task optimization. Current black-box multi-task algorithms only
solve a finite set of tasks, even when the tasks originate from a continuous
space. In this paper, we introduce Parametric-Task MAP-Elites (PT-ME), a new
black-box algorithm for continuous multi-task optimization problems. This
algorithm (1) solves a new task at each iteration, effectively covering the
continuous space, and (2) exploits a new variation operator based on local
linear regression. The resulting dataset of solutions makes it possible to
create a function that maps any task parameter to its optimal solution. We show
that PT-ME outperforms all baselines, including the deep reinforcement learning
algorithm PPO on two parametric-task toy problems and a robotic problem in
simulation.
