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Geometric regularity, which leverages data symmetry, has been successfullyincorporated into deep learning architectures such as CNNs, RNNs, GNNs, andTransformers. While this concept has been widely applied in robotics to addressthe curse of dimensionality when learning from high-dimensional data, theinherent reflectional and rotational symmetry of robot structures has not beenadequately explored. Drawing inspiration from cooperative multi-agentreinforcement learning, we introduce novel network structures for single-agentcontrol learning that explicitly capture these symmetries. Moreover, weinvestigate the relationship between the geometric prior and the concept ofParameter Sharing in multi-agent reinforcement learning. Last but not theleast, we implement the proposed framework in online and offline learningmethods to demonstrate its ease of use. Through experiments conducted onvarious challenging continuous control tasks on simulators and real robots, wehighlight the significant potential of the proposed geometric regularity inenhancing robot learning capabilities.

Learning Continuous Control with Geometric Regularity from Robot Intrinsic Symmetry