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 novel
black-box algorithm to solve 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
on two parametric-task toy problems and a more realistic and challenging
robotic problem in simulation that PT-ME outperforms all baselines, including
the deep reinforcement learning algorithm PPO.

利用相似性同时优化一组函数称为多任务优化。本文介绍参数化任务 MAP-Elites（PT-ME），一种解决连续多任务优化问题的新型黑盒算法。该算法每次迭代解决一个新任务，从而有效地覆盖连续空间，并利用基于局部线性回归的新型变异操作。在两个参数化任务玩具问题和一个更现实和具有挑战性的仿真机器人问题中，我们展示了 PT-ME 优于包括深度强化学习算法 PPO 在内的所有对照算法。