Hereditary Geometric Meta-RL: Nonlocal Generalization via Task Symmetries
arXiv:2603.00396v1 Announce Type: new Abstract: Meta-Reinforcement Learning (Meta-RL) commonly generalizes via smoothness in the task encoding. While this enables local generalization around each training task, it requires dense coverage of the task space and leaves richer task space structure untapped. In response, we develop a geometric perspective that endows the task space with a "hereditary geometry" induced by the inherent symmetries of the underlying system. Concretely, the agent reuses a policy learned at the train time by transforming states and actions through actions of a Lie group. This converts Meta-RL into symmetry discovery rather than smooth extrapolation, enabling the agent to generalize to wider regions of the task space. We show that when the task space is inherited from the symmetries of the underlying system, the task space embeds into a subgroup of those symmetries whose actions are linearizable, connected, and compact--properties that enable efficient learning a
arXiv:2603.00396v1 Announce Type: new Abstract: Meta-Reinforcement Learning (Meta-RL) commonly generalizes via smoothness in the task encoding. While this enables local generalization around each training task, it requires dense coverage of the task space and leaves richer task space structure untapped. In response, we develop a geometric perspective that endows the task space with a "hereditary geometry" induced by the inherent symmetries of the underlying system. Concretely, the agent reuses a policy learned at the train time by transforming states and actions through actions of a Lie group. This converts Meta-RL into symmetry discovery rather than smooth extrapolation, enabling the agent to generalize to wider regions of the task space. We show that when the task space is inherited from the symmetries of the underlying system, the task space embeds into a subgroup of those symmetries whose actions are linearizable, connected, and compact--properties that enable efficient learning and inference at the test time. To learn these structures, we develop a differential symmetry discovery method. This collapses functional invariance constraints and thereby improves numerical stability and sample efficiency over functional approaches. Empirically, on a two-dimensional navigation task, our method efficiently recovers the ground-truth symmetry and generalizes across the entire task space, while a common baseline generalizes only near training tasks.
Executive Summary
This article presents a novel approach to meta-reinforcement learning (Meta-RL) that leverages task symmetries to enable nonlocal generalization in the task space. The proposed method, Hereditary Geometric Meta-RL, assigns a geometric structure to the task space by transforming states and actions through actions of a Lie group. This approach allows the agent to generalize to wider regions of the task space, outperforming traditional Meta-RL methods. The method is demonstrated on a two-dimensional navigation task, where it efficiently recovers the ground-truth symmetry and generalizes across the entire task space. The results have significant implications for the field of Meta-RL, particularly in tasks that exhibit inherent symmetries.
Key Points
- ▸ Hereditary Geometric Meta-RL leverages task symmetries to enable nonlocal generalization in the task space.
- ▸ The proposed method assigns a geometric structure to the task space by transforming states and actions through actions of a Lie group.
- ▸ The approach allows the agent to generalize to wider regions of the task space, outperforming traditional Meta-RL methods.
Merits
Strength in leveraging task symmetries
The method's ability to leverage task symmetries provides a novel and effective approach to generalization in Meta-RL, enabling the agent to generalize to wider regions of the task space.
Efficient learning and inference
The proposed method enables efficient learning and inference at the test time due to the properties of the task space, including linearity, connectedness, and compactness.
Improved numerical stability and sample efficiency
The differential symmetry discovery method collapses functional invariance constraints, improving numerical stability and sample efficiency over functional approaches.
Demerits
Assumes inherent symmetries in the task space
The proposed method assumes the existence of inherent symmetries in the task space, which may not be the case in all tasks, limiting its applicability.
Requires additional computational resources
The method's reliance on Lie group actions and differential symmetry discovery may require additional computational resources, which could be a limitation in resource-constrained environments.
Expert Commentary
The proposed method presents a novel and effective approach to generalization in Meta-RL, leveraging task symmetries to enable nonlocal generalization in the task space. While the method assumes inherent symmetries in the task space, which may not be the case in all tasks, its ability to generalize to wider regions of the task space makes it a promising approach for tasks that exhibit such symmetries. The method's reliance on Lie group actions and differential symmetry discovery may require additional computational resources, but its potential benefits make it worth exploring further. The proposed method has significant practical implications for tasks such as robotic manipulation and navigation, and its policy implications are significant, particularly in tasks where the agent must adapt to changing environments or uncertainty.
Recommendations
- ✓ Further research is needed to investigate the applicability of the proposed method to tasks that do not exhibit inherent symmetries.
- ✓ The method's reliance on Lie group actions and differential symmetry discovery should be explored further to minimize computational resources and improve scalability.