GoIRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction

We sincerely appreciate the reviewer’s thorough and thoughtful feedback. We are grateful for the recognition of our work’s motivations, technical contributions, framework designs, and experimental results, as well as for the constructive suggestions for improvement. Below, we address each of the reviewer’s comments in detail.

1. Accuracy at Each Prediction Step. Thank you for your valuable suggestion. The following table (https://anonymous.4open.science/api/repo/Anonymous-F687/file/Tab1.png) presents the Displacement Error (DE) per prediction step for the forecasted trajectory. As expected, the model performs more accurately in the initial steps, with errors increasing in later steps. This trend aligns with the inherent uncertainty of long-horizon predictions. We will incorporate this analysis into the revised manuscript.

2. Recent Solutions & References. We greatly appreciate the reviewer’s recommendations for recent solutions. The referenced works propose different paradigms:

   • Ref. [1] employs a self-supervised approach leveraging all data (including the test set) for pertaining.
   • Ref. [2] introduces a powerful query-centric paradigm for scene encoding within a supervised learning paradigm.
   • Ref. [3] focuses on improving out-of-distribution generalization by introducing a novel evaluation protocol.

   Our approach differs in that it emphasizes a graph-based IRL framework to address covariate shift while maintaining competitive performance on standard trajectory prediction benchmarks. We will cite and discuss these works in the revised manuscript.

3. Model Inference Latency. Thank you for this important consideration. Our model achieves an average inference latency of approximately 30 ms on an NVIDIA RTX 3090 GPU using a standard PyTorch implementation. We will include this information in the revision.

4. Performance with Noisy Inputs. We appreciate the suggestion to evaluate our model’s robustness. To assess this, we introduced Gaussian noise with zero mean and varying standard deviations (STD) to the inputs. The results, summarized in the following table (https://anonymous.4open.science/api/repo/Anonymous-F687/file/Tab2.png), indicate that while significant noise degrades prediction accuracy, minor perturbations have minimal impact. This suggests that our model exhibits a degree of robustness to moderate input noise. We will include these findings into the revised manuscript.

5. Failure Cases. Thank you for the valuable suggestion to analyze failure cases. We provide several representative failure scenarios, which can be accessed at https://anonymous.4open.science/api/repo/Anonymous-F687/file/Figure1.jpg.

   • Figure 1(a) illustrates how poor observations of static or slow-moving agents can negatively impact trajectory predictions.
   • Figure 1(b) demonstrates that inaccuracies in speed prediction can affect longitudinal accuracy.
   • Figure 1(c) highlights a limitation where the model fails to predict a lane change in the absence of explicit cues.

   We believe these examples offer some insights into the conditions under which our model may struggle. These failure cases, along with a discussion of their potential causes, will be included in the revised manuscript.

6. Model Interpretability. We sincerely appreciate your insightful comment. Unlike fully supervised models that solely learn from data distributions, our graph-based IRL approach follows the MaxEnt IRL framework, which provides a learned reward function. This offers meaningful insights into the model’s decision-making process and allows for the integration of explicit constraints within the reward function, potentially enhancing interpretability. As discussed in Appendix C, we provide preliminary analysis on this aspect, and we recognize that further exploration of interpretability remains an important avenue for future research.

7. Grid Resolution for Different Scenes. Thank you for this instructive question. The choice of grid resolution involves a trade-off between efficiency and accuracy. In our implementation, we simply use a fixed grid resolution for both the Argoverse and nuScenes datasets, complemented by a refinement module to mitigate its impact. However, adapting the grid resolution to the specific driving scene could further improve performance.

References

[1] SEPT: Towards Efficient Scene Representation Learning for Motion Prediction.

[2] QCNeXt: A Next-Generation Framework for Joint Multi-Agent Trajectory Prediction.

[3] Improving Out-of-Distribution Generalization of Trajectory Prediction for Autonomous Driving via Polynomial Representations.

We sincerely appreciate the reviewer’s recognition of our research contributions and writing clarity, as well as the constructive feedback and valuable suggestions for improvement. Below, we address the reviewer’s concerns in detail.

1. Recent Trajectory Prediction Methods. Thank you for your thoughtful suggestions. We would like to clarify our choice of datasets. Since our work focuses on empowering IRL with vectorized representations, we selected Argoverse and nuScenes for evaluation based on benchmarking considerations: the graph-based model (DSP [1]) was originally evaluated on Argoverse, while P2T [2], to our knowledge, the only IRL-based trajectory predictor on the public leaderboard, was benchmarked on nuScenes. To ensure fair and meaningful comparisons, we adopted these two datasets as our benchmarks. Nonetheless, we acknowledge the importance of the Waymo dataset and will consider extending our experiments to Waymo in future work. Regarding autoregressive models for trajectory prediction, we include Autobot [3], an autoregressive approach on Argoverse, for comparison. As shown in the table below, our method remains competitive, demonstrating the effectiveness of IRL-based approaches. |Method|brier-minFDE$_{6}$|Brier score|minFDE$_{6}$|minADE$_{6}$|MR$_{6}$| |:-|:-:|:-:|:-:|:-:|:-:| |AutoBot|2.057|0.685|1.372| 0.876|0.164| |GoIRL (Ours)|1.796|0.623|1.173|0.809|0.120|

2. Qualitative Examples. We apologize for any confusion regarding our qualitative results. The scenarios presented in Figures 4, 5, and 7 include multiple traffic participants; however, for clarity, we omitted other agents to better highlight the target vehicle’s predictions. A more comprehensive visualization, including all agents, is available in the supplementary video. We will revise the manuscript to explicitly state this and include additional examples in the appendix to better illustrate interactive scenarios with multiple agents.

3. Loss Function. Thank you for your insightful comment. Our loss function follows a standard formulation for two-stage trajectory prediction models, comprising regression losses for both proposal and refined trajectories, along with a classification loss for probability estimation. In practice, we use fixed values of $\alpha=$ 1, $\beta=$ 1, and $\gamma =$ 3 in Eq. (12), which do not require extensive tuning across datasets. We will clarify this in the revised manuscript.

4. Covariate Shift Example in Figure 1. We appreciate the reviewer’s insightful comment and apologize for any confusion. The example in Figure 1 is intended to illustrate a covariate shift scenario in which the drivable area attribute changes. Herein, the barricade represents a constraint indicating that the region behind it is undrivable. In the training dataset, the model learns from observed drivable area annotations and the corresponding labels of ground-truth future trajectories. However, during testing, the drivable attribute is altered in the input while the ground-truth trajectory remains unchanged. This setup aligns with the definition of covariate shift [4], where the input distribution changes while the relationship between inputs and labels remains the same. We will clarify this more explicitly in the revision.

5. Query-Centric Representation. We greatly appreciate the reviewer’s insightful suggestion. Our IRL framework can indeed be integrated into a query-centric representation, and our ongoing work has demonstrated its feasibility in such settings. However, in this paper, our primary focus is on exploring the benefits of a graph-based representation. We will discuss the potential for extending our approach to query-centric representations in the future work section.

6. Ensemble Strategy. Thank you for your thoughtful inquiry. Our ensemble strategy follows a standard approach, where multiple models trained with different random seeds are combined using a weighted k-means algorithm to aggregate the forecasted trajectories. The results presented in Table 3 also incorporate this ensemble strategy, and we will explicitly clarify this point in the revised manuscript.

References

[1] Trajectory Prediction with Graph-based Dual-Scale Context Fusion.

[2] Trajectory Forecasts in Unknown Environments Conditioned on Grid-based Plans.

[3] Latent Variable Sequential Set Transformers for Joint Multi-Agent Motion Prediction.

[4] https://en.wikipedia.org/wiki/Domain_adaptation.

We sincerely appreciate the reviewer’s recognition of our work’s motivations, technical contributions, and experimental results, as well as the constructive suggestions for improvement. Below, we address the reviewer’s concerns in detail.

1. Choice of Benchmark Datasets & Recent Baselines.

We acknowledge the reviewer’s concerns regarding dataset and baseline selection and provide our response as follows:

(1) Fair Baseline Comparison. Our choice of Argoverse and nuScenes is primarily motivated by ensuring fair and meaningful comparisons within established benchmarks, as outlined below:

• Our supervised graph-based baseline (DSP [1]) was originally evaluated on Argoverse, ensuring a fair and rigorous comparison with our proposed IRL framework.
• To the best of our knowledge, nuScenes is the only large-scale benchmark featuring an IRL-based predictor (P2T [2]) on its public leaderboard. Since P2T employs rasterized images as input, evaluating our graph-based IRL model on nuScenes provides a valuable contrast.
• Despite being introduced in 2019 and 2020, Argoverse and nuScenes remain widely used, with strong baselines such as LOF [3] and QCNet [4] continuing to benchmark on them. The frequent public submissions further demonstrate their ongoing relevance.

(2) Comparison to Recent Baselines. Our model is the first IRL-based predictor with a vectorized representation, which primarily focuses on the comparison against other graph-based approaches and the IRL-based predictor with rasterized representations. As shown in the table below, our GoIRL model also achieves comparable brier-minFDE$_6$ and superior Brier score relative to strong supervised models (e.g., LOF & QCNet), demonstrating reliable predictions and competitive performance. As suggested, we will incorporate these recent baselines in our revised manuscript for a more comprehensive comparison.

(3) Contributions Beyond Benchmarks. Our work establishes a well-performing IRL-based baseline for trajectory prediction. While we acknowledge the importance of newer datasets, we believe our current evaluation is sufficient and reasonable to validate our contributions. Nevertheless, we plan to explore our method’s potential on additional benchmarks in future work.

2. Evaluation for Generalization in Drivable Area Changes.

We appreciate the reviewer’s concern regarding evaluation metrics and have conducted additional quantitative experiments to assess our model’s ability to generalize to drivable area changes. To the best of our knowledge, DSP is the only supervised model that incorporates drivable information. Therefore, we compare our method against DSP by evaluating the success rate across 150 diverse traffic scenarios, each with modified drivable attributes (as described in Section 4.3 of the paper). For each scenario, we randomly alter the drivable attributes near the future ground-truth positions 10 times, yielding 1,500 evaluation cases. The results, summarized in the table below, demonstrate that IRL-based predictors inherently learn interaction dynamics, leading to superior generalization in handling drivable area changes and mitigating domain bias. Moreover, we also provide additional qualitative examples to further illustrate the significance of addressing covariate shift, which can be accessed at https://anonymous.4open.science/api/repo/Anonymous-F687/file/case.jpg. These case studies demonstrate how our GoIRL model effectively handles covariate shifts in terms of drivable area changes in different scenarios.

References

[1] Trajectory Prediction with Graph-based Dual-Scale Context Fusion.

[2] Trajectory Forecasts in Unknown Environments Conditioned on Grid-based Plans.

[3] FutureNet-LOF: Joint Trajectory Prediction and Lane Occupancy Field Prediction with Future Context Encoding.

[4] Query-Centric Trajectory Prediction.

We sincerely appreciate the reviewer’s affirmative comments on the experimentation, results, and writing, as well as constructive suggestions and valuable references, which have helped us strengthen our manuscript. Below, we provide detailed responses to each of the concerns.

1. Clarification of the Statement in Figure 1. Thank you for your insightful comments. In fact, the motivating example in Figure 1 is abstracted from a real-world scenario in the Argoverse dataset (please see Figure 5 in the paper), where the original ground-truth trajectory follows a straight path. This example illustrates the necessary adaptations a predictor should make when encountering drivable area changes in the driving environment. If the ground-truth trajectory involved a left turn, we would modify the undrivable region at the left-turn entrance accordingly to reflect such domain bias issues. We will clarify this more explicitly in the revised manuscript.

2. Handling Drivable Area Changes. We appreciate the reviewer’s concern and would like to further clarify our motivation. Our work focuses on handling drivable area attributes, which differ from object-level obstacles (with tracking IDs or bounding boxes). For instance, certain undetectable obstacles, such as regions behind traffic barricades, may appear empty but remain undrivable due to implicit road rules or physical constraints. In practice, drivable area information can be obtained through techniques like occupancy prediction; in our work, we derive it from HD map annotations in the dataset. Our IRL-based method is designed to handle scenarios where drivable attributes differ from those observed during training, and we will clarify this distinction more explicitly in the revised manuscript.

3. Deterministic Prediction. Many thanks for your constructive comment. Our work primarily focuses on multimodal trajectory prediction due to the inherent uncertainty in future intentions. However, we recognize that deterministic prediction remains important. We appreciate the suggested reference (SingularTrajectory [1]) and will include it in our discussion, along with additional experimental results for k=1 in our revised version, as presented in the table below: |Dataset|minFDE$_{1}$|minADE$_{1}$|MR$_{1}$| |:-|:-:|:-:|:-:| |Argoverse|3.365|1.551|0.539| |nuScenes|6.530|3.185|0.822|

4. Control-Point Based Prediction. We thank the reviewer for sharing the excellent work, Graph-TERN [2], which presents a similar approach to trajectory representation. We will include it in our references and acknowledge its relevance in the revised manuscript.

5. Distinction from Existing IRL-Based Predictors. We greatly appreciate the reviewer’s valuable suggestion. The key novelty of our approach, compared to prior IRL-based predictors, lies in the representation and processing of driving context. Unlike previous IRL-based methods [3, 4, 5] that rely on rasterized imagery inputs, our method employs a vectorized (graph-based) representation, enabling it to capture geometric and semantic information in traffic scenes more effectively. Moreover, prior works such as [4,5] primarily focus on animal trajectory prediction, where motion dynamics differ significantly from those in human-driven traffic scenarios.

6. Contribution of Bézier Curve Parameterization. We greatly appreciate the reviewer’s detailed feedback. The primary motivation for adopting Bézier curve-based trajectory parameterization is to ensure kinematic feasibility, rather than solely improving trajectory prediction accuracy. While the performance improvement in standard metrics may be marginal, Bézier curves provide smooth, physically plausible trajectories that align with real-world motion constraints. We will clarify this reasoning in the revised manuscript.

7. Clarification of Table 4. Many thanks for your valuable suggestion. Table 4 presents an ablation study quantifying the impact of key components in our trajectory decoder. Each row removes a specific component to isolate its contribution to the overall performance and the last row represents the complete model, incorporating all components. We will make a clear statement in the revised version.

References

[1] SingularTrajectory: Universal Trajectory Predictor Using Diffusion Model.

[2] A Set of Control Points Conditioned Pedestrian Trajectory Prediction.

[3] Trajectory Forecasts in Unknown Environments Conditioned on Grid-based Plans.

[4] Travel Time-dependent Maximum Entropy Inverse Reinforcement Learning for Seabird Trajectory Prediction.

[5] Can AI Predict Animal Movements? Filling Gaps in Animal Trajectories using Inverse Reinforcement Learning.

We sincerely appreciate the reviewer’s thorough and professional evaluation of our work. We are grateful for the recognition of our work’s motivations, novelty, contributions, and experimental validation, as well as for the constructive feedback and valuable suggestions for improvement. Below, we provide detailed responses to each of the reviewer’s comments.

1. Choice of Datasets. Thank you for your thoughtful suggestion regarding additional datasets. Our current evaluation focuses on Argoverse and nuScenes, as these datasets have been widely used to benchmark graph-based trajectory prediction methods. Specifically, we selected Argoverse to benchmark against graph-based models and nuScenes to compare against P2T, which, to our knowledge, is the only IRL-based trajectory predictor on the public leaderboard. Ensuring fair and meaningful comparisons was our primary motivation for this choice. Nevertheless, we acknowledge the importance of evaluating on more diverse datasets to better demonstrate the effectiveness of our approach and we will explore extending our experiments to diverse datasets in future work.

2. Additional Baselines. We appreciate the reviewer’s valuable recommendation to include additional baselines for completeness. In the revised manuscript, we will incorporate comparisons with HiVT [1] and GANet [2], as well as grid-based motion prediction methods such as THOMAS [3], HOME [4], and GOHOME [5]. The table below presents the performance comparison: |Method|brier-minFDE$_{6}$|Brier score|minFDE$_{6}$|minADE$_{6}$|MR$_{6}$| |:-|:-:|:-:|:-:|:-:|:-:| |HiVT|1.842|0.673|1.169|0.774|0.127| |GANet|1.790|0.629|1.161|0.806|0.118| |THOMAS|1.974|0.535|1.439|0.942|0.104| |GOHOME|1.983|0.533|1.450|0.943| 0.105| |HOME+GOHOME|1.860|0.568|1.292| 0.890|0.085| |GoIRL (Ours)|1.796|0.623|1.173|0.809|0.120| |GoIRL-Ens (Ours)|1.695|0.569|1.126|0.783|0.110|

3. Additional Case Studies on Covariate Shift. Thank you for your insightful suggestion. To further illustrate the significance of addressing covariate shift, we provide additional qualitative examples, which can be accessed at https://anonymous.4open.science/api/repo/Anonymous-F687/file/case.jpg. These case studies demonstrate how our GoIRL model effectively handles covariate shifts in terms of drivable area changes in different scenarios.

References

[1] HiVT: Hierarchical Vector Transformer for Multi-Agent Motion Prediction.

[2] GANet: Goal Area Network for Motion Forecasting.

[3] THOMAS: Trajectory Heatmap Output with Learned Multi-Agent Sampling.

[4] HOME: Heatmap Output for Future Motion Estimation.

[5] GOHOME: Graph-Oriented Heatmap Output for Future Motion Estimation.