Geometric regularity, which leverages data symmetry, has been successfully incorporated into deep learning architectures such as CNNs, RNNs, GNNs, and Transformers. While this concept has been widely applied in robotics to address the curse of dimensionality when learning from high-dimensional data, the inherent reflectional and rotational symmetry of robot structures has not been adequately explored. Drawing inspiration from cooperative multi-agent reinforcement learning, we introduce novel network structures for single-agent control learning that explicitly capture these symmetries. Moreover, we investigate the relationship between the geometric prior and the concept of Parameter Sharing in multi-agent reinforcement learning. Last but not the least, we implement the proposed framework in online and offline learning methods to demonstrate its ease of use. Through experiments conducted on various challenging continuous control tasks on simulators and real robots, we highlight the significant potential of the proposed geometric regularity in enhancing robot learning capabilities.

翻译：几何规律性利用数据的对称性，已成功融入深度学习架构中，例如CNN、RNN、GNN和Transformer。尽管这一概念在机器人学中已被广泛应用于解决高维数据学习中的维度灾难问题，但机器人结构固有的反射和旋转对称性尚未得到充分探索。受多智能体协作强化学习的启发，我们引入了新颖的网络结构，用于单智能体控制学习，这些结构能够显式捕获这些对称性。此外，我们研究了几何先验与多智能体强化学习中参数共享概念之间的关系。最后但同样重要的是，我们将所提出的框架应用于在线和离线学习方法中，以展示其易用性。通过在模拟器和真实机器人上执行的各种挑战性连续控制任务上进行的实验，我们突显了所提出的几何规律性在增强机器人学习能力方面的巨大潜力。