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 deep learning algorithms that explicitly capture this geometric regularity. Moreover, we investigate the relationship between the geometric prior and the concept of Parameter Sharing in multi-agent reinforcement learning. Through experiments conducted on various challenging continuous control tasks, we demonstrate the significant potential of the proposed geometric regularity in enhancing robot learning capabilities.

翻译：几何正则性通过利用数据对称性，已成功融入卷积神经网络（CNN）、循环神经网络（RNN）、图神经网络（GNN）及Transformer等深度学习架构中。尽管该概念在机器人领域被广泛用于应对高维数据学习中的维度灾难问题，但机器人结构的固有反射与旋转对称性尚未得到充分探索。受协作多智能体强化学习启发，我们为深度学习算法引入能够显式捕获该几何正则性的新型网络结构。此外，我们探讨了几何先验与多智能体强化学习中参数共享概念的内在关联。通过在多种具有挑战性的连续控制任务上的实验，我们验证了所提出的几何正则性在增强机器人学习能力方面的显著潜力。