Summary
The paper introduces the Equivariant Diffuser for Generating Interactions (EDGI), an $SE(3)\times \mathbb{Z} \times S_n$-equivariant diffusion model for model-based reinforcement learning. The proposed method maintains equivariance with spatial symmetry as depicted by $SE(3)$, the discrete time translation symmetry signified by $\mathbb{Z}$, and the object permutation symmetry symbolized by $S_n$. The paper further theoretically analysis on the conditions under which the samples from an equivariant diffusion model will be group invariant or symmetry-breaking. Finally, experimental evaluations were conducted in both manipulation and navigation tasks, demonstrating that the proposed method surpasses the performance of non-equivariant baselines.
Strengths
1. The method considers a large variety of symmetries, all of which are common in many robotic tasks.
2. The concept of using a sequence of three equivariant layers to handle the three distinct symmetries is novel and intriguing.
3. The generalization experiment demonstrates convincing results.
Weaknesses
The experiment section could be more comprehensive.
First, the paper does not provide an ablation study to justify the three symmetries considered. Will removing one or two of the symmetries harms the performance? Which of the three symmetries contributes the most to the success of the architecture?
Second, a data augmentation baseline can also be considered. Though it is widely demonstrated that the equivariant network architecture normally performs better than the learned equivariance through data augmentation, it is still a valuable experiment to validate the proposed network architecture. Moreover, will data augmentation + equivariant network yield even better performance?
Questions
1. Although the proposed sequential approach for handling three different types of symmetries is conceptually sound, a theoretical understanding would be beneficial. Specifically, can the author provide a theoretical analysis that the operation on one of the three equivariant layers will not influence the other two equivariant properties?
2. In some of the experiments (e.g., Navigation in Table 1), EDGI does not significantly outperforms the baseline Diffuser. This is different from what normally is observed in the equivariant learning literature when comparing an equivariant approach vs. a non-equivariant approach. It would be helpful if the authors could provide some analysis on this.
3. Why is the hidden layer in the form of $\rho_0 \oplus \rho_1$? Will adding higher frequency signal in the hidden layer (i.e., $\oplus_0^k \rho_k$ where $k>1$) improve the performance?
4. Some figures of the experimental domains would be helpful (at least in the appendix) to better understand the environments.
Rating
6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
Confidence
4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Limitations
The paper addresses its limitation, but the discussion could be expanded. For instance, the proposed method seems highly constrained on the input data type, which could make it challenging to extend the proposed method to visual inputs.