What If You Were Not There? Learning Causally-Aware Representations of Multi-Agent Interactions

Dear Reviewer FV83,

Thank you for your insightful feedback. Please find our response to your comments below.

The assumption that the underlying causal mechanisms stay the same between the simulation and real-world is simply too fragile to be true. For example, ignoring the fact that drivers also check rearview mirrors.

• We acknowledge your concern and clarify that we do not assume all causal mechanisms stay the same. Instead, we assume they differ between the simulation and real-world in a sparse way (cf. sparse mechanism shift [1,2]). For the mechanisms shared across the two domains, we can first annotate them in the simulation and further transfer them to the real-world.
• This assumption aligns well with our considered setting, where the simulator is designed and calibrated to mimic pedestrian behaviors (not drivers) in the real-world, including a 210-degree field of view to match human visual perception [3].
• To the best of our knowledge, existing research in causal representation learning is still confined to synthetic/simulated settings, and struggles to scale to the real-world. Our proposed sim-to-real causal transfer provides a new perspective to bridge this gap and may hold great promise in broader settings beyond the considered application.

Could you report all three metrics for figure 6 and 8?

• We’d like to clarify that it is not possible to evaluate ACE for Figure 8, due to the absence of causal annotations in the real-world ETH-UCY dataset.
• We have added FDE for Figure 6 into the appendix (Figure 9). We didn’t report it in the previous version, because the pattern of FDE is similar to that of ADE and does not provide much additional information.

We do see notable improvements of the “rank” method over baselines but I am not sure if it’s a fair comparison because the “rank” method actually provides way more labeling information than binary labels (causal/non-causal).

• We’d like to clarify that the goal of the experiment is not about which method is better given the same annotations. Instead, we aim to examine the relative benefits of fine-grained annotations over coarse-grained labels, as noted at the beginning of the experiment section (Q3).
• Our result shows that learning from fine-grained annotations through a ranking regularizer yields substantial improvements over the other counterparts. This result provides valuable guidance for causal annotation strategies in simulation and real-world scenarios.

At last, when using 100% percent data in the sim-to-real test, the proposed method (contrast) barely beats those baselines leaving doubts on whether the performance gaps in 25% and 50% scenarios are due to learning efficiency difference instead of representation quality.

• We appreciate your observation regarding the performance gaps in different data scenarios. We’d like to clarify that we do not claim superiority of our contrastive variant over the augment baseline; their performance is comparable across most experiments. The main finding we’d like to highlight is the strength of our ranking-based variant, including its high learning efficiency in the low data regime, e.g., reaching similar or even better accuracies with 1/2 less of the real-world data.

Could you extend the experiments to multiple random seeds and report the variances in the figures?

Thank you for the suggestion.

• We have updated Figure 6 in our manuscript to report the variance across 5 random seeds.
• We are still running the experiments on different seeds for Figure 8. Below are the preliminary results on the full (100%) ETH-UCY dataset. We anticipate completing the experiments by next week and will update Figure 8 accordingly.

[1] Towards Causal Representation Learning, 2021
[2] From Statistical to Causal Learning, 2022
[3] Seven Myths on Crowding and Peripheral Vision, 2020

Thank you for your detailed response. Most of my concerns have been clarified. I am looking forward to more experiment results about Fig. 8. However, I would like to pose three follow up questions based on your response.

1. From the current table, it seems that "ranking" is still not completely beating the baselines, which casts doubts on "the strength of our ranking-based variant". Is this a contradiction to your claim?

2. Though the references the authors provided are not formatted, I managed to find the papers, which I believe should be the right ones. It seems that the sparse mechanism shift is defined under the Causal Markov Condition, which basically means that there will be no unobserved confounders. I am not sure if it is realistic to model the pedestrian behaviors assuming that there are no spurious correlations among them. And this question could have been better clarified if the author had defined the type of causal model they were using exactly with the formal causal language [1].

3. If the dataset is all about pedestrian behaviors, Fig 2 seems to be misleading since in that figure the ego agent is a car instead of a pedestrian.

Dear Reviewer FV83,

We would like to reiterate the three main contributions of our submission.

1. Reveal the annotation and evaluation issues in the recent large-scale CausalAgent benchmark
2. Introduce a causal metric learning approach that boosts causal awareness and out-of-distribution robustness in controlled simulations
3. Propose a sim-to-real causal transfer technique that yields encouraging results without relying on real-world annotations and thus holds great promise for practical problems

We acknowledge the limitations of our study, as you rightly pointed out, and have explicitly discussed some of them in the Limitations and Additional Discussions paragraphs in our manuscript.

Given these contributions and discussions, we respectfully disagree with your conclusion that our submission should be rejected, and we believe that it fills critical knowledge gaps in the field.

Finally, we would like to express our sincere gratitude for the time and effort that you have invested in reviewing our work.

Regarding my point 2 previously, modeling the causal effect rigorously should be the foundation of the problem instead of a “fascinating future work”. And if you check the references you provided, they clearly stated in the context that they described the sparse mechanism shift under the markovian causal model, where there is no confounders. Citing another vague statement does not help in this case since there are already established causal literatures solving this exactly. You may refer to the line of transportability in causal inference for more details.

Regarding my point 3, as the authors stated in their previous response, the simulator they used “models the behavior of pedestrians” not “drivers”. If your goal is to “explore casually aware representations in a broad multi agent setting”, you should include more general simulators instead of a pedestrian simulator and should not assuming that there are no confounders between the agents behavior. Again, this confusion is also partially due to the problem that the authors failed to model the problem using precise causal language properly.

Thus, I’ll keep the score.

Dear Reviewer 1Bm7,

Thank you for your insightful feedback. Please find our response to your comments below.

It would be appreciated if the authors could provide justification for their annotation process and evaluation metric which is based on the influence measured by removing a single agent.

• Indeed, the causal effect in the multi-agent context can be studied at both the individual agent level (removing one agent at a time) and the group level (removing a group of multiple agents). Our focus on agent-level causal effects was motivated by two factors:
  • It aligns with the notion of Causal Agents, i.e., a neighboring agent has a certain causal relationship with the ego agent. This allows us to revisit the root cause of the robustness issues in the prior benchmark.
  • It permits efficient experiments, i.e., studying causal effects at the agent level presents a linear computational complexity O(N), whereas studying that at the group level could lead to an exponential increase in complexity, up to O(2^N).
• Having said that, we acknowledge that exploring the latter can be an exciting avenue for future research. We have updated our manuscript to reflect this perspective, framing our finding about partially robust in the context of agent-level causal effects and discussing its limitation in Appendix C.

How the proposed regularization strategy would work on other datasets and with other backbone methods.

• We are currently running experiments on another backbone (D-LSTM) benchmarked in Tab 1. Our preliminary result shows larger performance gains on D-LSTM than on AutoBots. We anticipate completing the experiments soon and will update our response accordingly.

Lacks a detailed description of the proposed diagnostic dataset. For example, what is the difference between OOD-Context and OOD-Density-Context? Maybe a figure or illustration would be much appreciated.

• The key difference between OOD-Context and OOD-Density-Context is that the former introduces major changes in scene contexts, whereas the latter introduces more significant increases in the number of causal agents as well as modest changes in scene contexts.
• As per your suggestion, we have added a more detailed description in the dataset details paragraph in Appendix B, along with animations in our public repository for better illustration.

Fig 2 is not color friendly (it is hard to distinguish cyan and blue).

• Thank you for bringing this to our attention. We have updated the figure, changing blue to red.

The paper sometimes interchangeably uses “causal representation” and “causally-aware representation”. I think the latter fits the paper.

• Thank you for the suggestion. We have revised the manuscript, using the term “causally-aware representation” more uniformly across the paper.

Dear Reviewer d8CZ,

Thank you for your insightful feedback. Please find our response to your comments below.

The proposed approach seems to provide marginal improvements across all metrics

• We would like to highlight that our method was evaluated on a state-of-the-art baseline, where significant leaps in performance are inherently challenging. Despite this, our ranking-based method yields ~10% performance gain on several metrics, e.g., ACE in the low-quantile causal effect scenarios and ADE in the OOD density and context settings. Most notably, the final version of our method enables the model to reach better accuracy while requiring only half the real-world data.

It would be much more interesting if the ACE metrics in Table 1 were replicated with the proposed approaches, showing how these values (particularly ACE-DC/IC) are presumably improved. Why is the split done using quantiles here instead of spliting across the ACE-X metrics?

• The quantile split was chosen to better understand the strengths and limits of the proposed method in causal effect estimates. As shown in Fig 6a, the improvement over ACE is greater with smaller ground-truth causal effects. We conjecture this is in large part due to the imperfect decoding process.
  • When the causal effect of the neighboring agent is small (affects the ground-truth trajectory only locally), encoding the paired scenes into nearby embeddings results in similar prediction outputs and hence small ACE, canceling out the influence of the decoding error.
  • In contrast, when the causal effect of the neighboring agent is large (affects the ground-truth trajectory at macro scale), even if encoding the paired scenes into properly separated embeddings, the decoding errors of each trajectory may compound and lead to large ACE.
• Following your suggestion, we have extended our evaluation to include ACE-DC and ACE-IC metrics. The results are summarized in Figure 10 in our updated manuscript. Our proposed method yields comparable improvements on the two metrics. We conjecture this is because our proposed method treats DC and IC agents uniformly.

Figure 4 is not referenced anywhere.

• Thank you for bringing it to our attention! In our updated manuscript, we have added reference to Fig 4 in the paragraph right after Eq 5.

In Figure 8, what is the difference between baseline and vanilla?

• The baseline refers to training the model on real-world data only, whereas the vanilla sim-to-real refers to training the model on simulated and real-world data jointly. In our updated manuscript, we elaborate on the details of each method in the baseline details paragraph in Appendix B.

If I understood correctly, augment is the data augmentation baseline, and baseline is actually vanilla Autobots. Is this correct?

• Yes, the baseline refers to the original Autobots throughout our manuscript, whereas the augment refers to the causal data augmentation technique in Roelofs el al. 2022. We have updated figure captions accordingly in our updated manuscript.

I wonder if it would be interesting to also look at the number(or percentage) of ego-collisions in the sim-to-real experiments.

• Thank you for the suggestion. Our method does not significantly reduce collision rates compared to the baseline. This is because the AutoBots baseline already exhibits exceptionally low collision rates on the ETH-UCY dataset (0.5%), leaving marginal room for improvements.

What exactly is the unseen context variant in the OOD experiments?

• The training context comprises a simulated open area with randomized agent directions, whereas the OOD context features a simulated street with constrained agent movements. Please refer to more detailed description in the dataset details paragraph in Appendix B, along with animations in our public repository for illustration.

Thank you for your insightful comments. Please find our clarifications below.

Assumptions Underlying Causally-Aware Representations: causal relationships capture multi-agent interactions

• Our work posits that desired representations of multi-agent interactions should capture the causal relationship between behaviors of interactive agents. For instance, consider a scenario where two agents walk in a line, their similarity in pace is not just a statistical correlation but governed by an asymmetric causal relationship, i.e., the agent in front casually influences the agent behind, but not the other way around. This example highlights our belief in the significance of causal relationships for modeling multi-agent interactions. We are open to further discussion and clarification on this point.

Difference and Connection with Causal Representation: how the proposed method aligns with or differs from it

• Connection: To our knowledge, the essence of causal representations lies in capturing causal dependencies over statistical correlations. Our work resonates with this principle, i.e., we seek to build an abstract representation of multi-agent interactions that captures the causal relationship between individual agents, as opposed to the spurious correlations in the training data (e.g., agent density vs. interaction intensity).
• Difference: Unlike previous studies that often focus on identifying causal variables (and structures) in the data generating process, we relax the strict requirement of identifiability and instead place more emphasis on its practical implications, e.g., our proposed sim-to-real causal transfer framework, which seeks to mitigate the absence of real-world causal annotations.
• Reference: We appreciate the reference that you suggested and enjoyed reading these papers on causal representation learning for domain adaptation. Nevertheless, given that our work is positioned in the multi-agent context with an emphasis on out-of-distribution generalization, we believe that the literature cited in our related work section is more directly pertinent to the main focus of our work.

Data Sufficiency for Experiments: simulating the trajectories could be helpful in this aspect, such as CausalCity.

• Yes, we fully agree. In fact, this perspective has been integral to the curation of our diagnostic dataset, for which we intervened one agent at a time to obtain counterfactual data pairs, as detailed in Section 3.3.
• While our work opted for ORCA as a minimalist yet effective simulator of multi-agent interactions, we acknowledged the potential benefits of using more advanced simulators like CausalCity in future research, as discussed in Appendix C.