Learning skills by imitation is a promising concept for the intuitive teaching of robots. A common way to learn such skills is to learn a parametric model by maximizing the likelihood given the demonstrations. Yet, human demonstrations are often multi-modal, i.e., the same task is solved in multiple ways which is a major challenge for most imitation learning methods that are based on such a maximum likelihood (ML) objective. The ML objective forces the model to cover all data, it prevents specialization in the context space and can cause mode-averaging in the behavior space, leading to suboptimal or potentially catastrophic behavior. Here, we alleviate those issues by introducing a curriculum using a weight for each data point, allowing the model to specialize on data it can represent while incentivizing it to cover as much data as possible by an entropy bonus. We extend our algorithm to a Mixture of (linear) Experts (MoE) such that the single components can specialize on local context regions, while the MoE covers all data points. We evaluate our approach in complex simulated and real robot control tasks and show it learns from versatile human demonstrations and significantly outperforms current SOTA methods. A reference implementation can be found at https://github.com/intuitive-robots/ml-cur

翻译：通过模仿学习技能是机器人直观教学的一个有前景的概念。学习此类技能的一种常见方法是最大化给定示范数据下的似然函数来学习参数模型。然而，人类示范往往具有多模态性，即同一任务可通过多种方式完成，这对大多数基于最大似然（ML）目标的模仿学习方法构成了重大挑战。ML目标迫使模型覆盖所有数据，阻碍了其在上下文空间中的专业化，并可能导致行为空间中的模式平均化，从而引发次优甚至灾难性的行为。本文通过引入基于每个数据点权重的课程来缓解这些问题，使模型能够专注于其可表示的数据，同时通过熵奖励激励其尽可能覆盖更多数据。我们将算法扩展至混合线性专家模型（MoE），使得单个组件能够专注于局部上下文区域，而MoE则覆盖所有数据点。我们在复杂的仿真和真实机器人控制任务中评估了该方法，结果表明其能从多样化的人类示范中学习，并显著优于当前最先进方法。参考实现详见https://github.com/intuitive-robots/ml-cur