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.

翻译：参数化任务MAP-Elites算法。同时优化一组函数并利用它们之间的相似性被称为多任务优化。现有的黑箱多任务算法即使任务源自连续空间，也只能解决有限的任务集合。本文提出参数化任务MAP-Elites（PT-ME），一种用于解决连续多任务优化问题的新型黑箱算法。该算法：(1) 在每次迭代中求解一个新任务，有效覆盖连续空间；(2) 利用基于局部线性回归的新型变异算子。由此产生的解数据集能够构建一个将任意任务参数映射到其最优解的函数。我们在两个参数化任务玩具问题和一个更接近现实且具有挑战性的仿真机器人问题上证明，PT-ME在所有基线方法中表现最优，包括深度强化学习算法PPO。