DreamSAC: Learning Hamiltonian World Models via Symmetry Exploration
This work aims to improve the extrapolative generalization of world models for agents operating in physical environments, which is a significant problem for robotics and simulation.
This paper addresses the limitation of learned world models in extrapolating to novel physical properties by learning underlying physical invariances and conservation laws. They introduce Symmetry Exploration, an unsupervised strategy using a Hamiltonian-based curiosity bonus to collect physically informative data, and a Hamiltonian-based world model with a self-supervised contrastive objective. The DreamSAC framework, trained on this data, significantly outperforms state-of-the-art baselines in 3D physics simulations on extrapolation tasks.
Learned world models excel at interpolative generalization but fail at extrapolative generalization to novel physical properties. This limitation arises because they learn statistical correlations rather than the environment's underlying generative rules, such as physical invariances and conservation laws. We argue that learning these invariances is key to robust extrapolation. To achieve this, we first introduce \textbf{Symmetry Exploration}, an unsupervised exploration strategy where an agent is intrinsically motivated by a Hamiltonian-based curiosity bonus to actively probe and challenge its understanding of conservation laws, thereby collecting physically informative data. Second, we design a Hamiltonian-based world model that learns from the collected data, using a novel self-supervised contrastive objective to identify the invariant physical state from raw, view-dependent pixel observations. Our framework, \textbf{DreamSAC}, trained on this actively curated data, significantly outperforms state-of-the-art baselines in 3D physics simulations on tasks requiring extrapolation.