Leveraging Symmetry in Dynamics for Efficient Model-Based Reinforcement Learning with Asymmetric Rewards

Core Concepts

By exploiting symmetries in the dynamical model, independent of the reward function, this work presents a method to learn more accurate dynamical models that can improve sample efficiency in model-based reinforcement learning.

Abstract

The paper investigates scenarios where only the dynamics exhibit symmetry, independent of the reward function. This extends the scope of problems in reinforcement learning and control theory where symmetry techniques can be applied.
The key highlights are:

The authors use Cartan's moving frame method to introduce a technique for learning dynamics which, by construction, exhibit specified symmetries. This allows encoding a priori known symmetry structure when learning a dynamical model.

The proposed method learns a function ¯F that maps the lower-dimensional reduced state space to the next state, rather than learning the full dynamics F directly. This reduces the input dimensionality and improves learning efficiency.

Numerical experiments on the "Parking" and "Reacher" environments demonstrate that the symmetry-based method learns more accurate dynamical models, especially when the neural network has fewer parameters, compared to learning the full dynamics without exploiting symmetry.

The authors show that their approach can be applied even when only the dynamics exhibit symmetry, while the reward function does not, which is a more general setting than previous work that assumed both dynamics and rewards are symmetric.

Stats

The dynamics of the cart-pole system are invariant to the position of the cart.
The dynamics of the reacher environment exhibit rotational symmetry with the first joint angle.

Quotes

"A commonly used simplifying assumption is that the dynamics and reward both exhibit the same symmetry. However, in many real-world environments, the dynamical model exhibits symmetry independent of the reward model: the reward may not satisfy the same symmetries as the dynamics."
"Exploiting symmetries only in the dynamical model widens the scope of RL problems to which symmetry can be applied."

Key Insights Distilled From

Exploiting Symmetry in Dynamics for Model-Based Reinforcement Learning with Asymmetric Rewards

by Yasin Sonmez... at arxiv.org 03-29-2024

https://arxiv.org/pdf/2403.19024.pdf

Deeper Inquiries

How can the proposed symmetry-based method be extended to handle more complex symmetry groups beyond the continuous groups considered in this work

The proposed symmetry-based method can be extended to handle more complex symmetry groups by incorporating techniques from group theory and differential geometry. One approach is to consider Lie groups with higher dimensions, allowing for more intricate transformations beyond simple rotations and translations. By utilizing advanced mathematical tools, such as Lie algebra and representation theory, the method can be adapted to capture a broader range of symmetries present in complex dynamical systems. Additionally, exploring non-continuous symmetries, such as discrete symmetries or non-Abelian groups, would further enhance the method's applicability to a wider variety of systems.

What are the potential limitations or drawbacks of relying on a priori known symmetries when the true symmetries of the system are not fully known or may change over time

Relying on a priori known symmetries can pose limitations when the true symmetries of the system are not fully understood or may evolve over time. One potential drawback is the risk of model misspecification if the assumed symmetries do not accurately reflect the underlying dynamics. This mismatch can lead to suboptimal performance or even instability in the learned models. Moreover, the computational complexity of identifying and incorporating all possible symmetries a priori can be challenging, especially in highly complex or unknown environments. Adapting the method to dynamically learn and update symmetries based on observed data could mitigate these limitations and enhance the method's robustness in real-world applications.

Could the insights from this work on leveraging asymmetric rewards be combined with other techniques, such as meta-learning or transfer learning, to further improve sample efficiency in model-based reinforcement learning

Combining insights from leveraging asymmetric rewards with meta-learning or transfer learning techniques can offer significant benefits in improving sample efficiency in model-based reinforcement learning. Meta-learning algorithms can adapt the model learning process to different environments or tasks by leveraging prior knowledge and experience, enabling faster adaptation and generalization. By integrating asymmetric rewards into meta-learning frameworks, the agent can learn to exploit asymmetries in the reward structure to optimize policy performance efficiently across diverse scenarios. Transfer learning can further enhance sample efficiency by transferring knowledge and policies learned from one task to accelerate learning in related tasks with asymmetric rewards. This integration of techniques can lead to more adaptive and efficient reinforcement learning systems capable of handling complex and dynamic environments effectively.