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.
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