GoIRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction
Authors: Muleilan Pei
Shaoshuai Shi
Lu Zhang
Peiliang Li
Shaojie Shen
Venue: ICML 2025 poster (2025)
Keywords: Autonomous Driving
Trajectory Prediction
Inverse Reinforcement Learning
Primary area: applications->computer_vision
TL;DR: A novel trajectory predictor integrating the inverse reinforcement learning paradigm with vectorized context representations.

Abstract: Trajectory prediction for surrounding agents is a challenging task in autonomous driving due to its inherent uncertainty and underlying multimodality. Unlike prevailing data-driven methods that primarily rely on supervised learning, in this paper, we introduce a novel **G**raph-**o**riented **I**nverse **R**einforcement **L**earning (GoIRL) framework, which is an IRL-based predictor equipped with vectorized context representations. We develop a feature adaptor to effectively aggregate lane-graph features into grid space, enabling seamless integration with the maximum entropy IRL paradigm to infer the reward distribution and obtain the policy that can be sampled to induce multiple plausible plans. Furthermore, conditioned on the sampled plans, we implement a hierarchical parameterized trajectory generator with a refinement module to enhance prediction accuracy and a probability fusion strategy to boost prediction confidence. Extensive experimental results showcase our approach not only achieves state-of-the-art performance on the large-scale Argoverse & nuScenes motion forecasting benchmarks but also exhibits superior generalization abilities compared to existing supervised models.

GoIRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction
Muleilan Pei
Shaoshuai Shi
Lu Zhang'
Peiliang Li
Shaojie Shen
Abstract
Trajectory prediction for surrounding agents is a challenging task in autonomous driving due its inherent uncertainty and underlying multimodal- ity. Unlike prevailing data-driven methods that primarily rely supervised learning. in this pa- per, we introduce novel Graph-oriented Inverse Reinforcement Learning (GoIRL) framework, which is an IRL-based predictor equipped with vectorized context representations. We develop feature adaptor to effectively aggregate lane- graph features into grid space, enabling seam- less integration with the maximum entropy IRL paradigm to infer the reward distribution and ob- tain the policy that can be sampled to induce mul- tiple plausible plans. Furthermore, conditioned on the sampled plans, we implement a hierarchi- cal parameterized trajectory generator with finement module to enhance prediction accuracy and a probability fusion strategy to boost predic- tion confidence. Extensive experimental results showcase our approach not only achieves state-of- the-art performance on the large-scale Argoverse & nuScenes motion forecasting benchmarks but also exhibits superior generalization abilities com- pared to existing supervised models.
Figure 1. A motivating example of the covariate shift issue in tra- jectory prediction. T-junction driving scenario, the target agent has two potential future trajectories: going straight and turning left. During the data collection process, ground-troe -tuut trajectory labeled as going straight. However, during testing, the presence of tentative barricade set up intersection renders the original prediction unreasonable. Hence, the predictor must adapt to this change and provide an updated prediction, considering only the option of turning left in this case.
autonomous vehicles can make safe, efficient, and judicious decisions intricate urban scenarios. However, the task of motion forecasting remains challenging because of its inherent uncertainty and underlying multimodality: agent exhibit multiple plausible future trajectories given its past tracks and the available scene information (Song et al., 2021; Shi et al., 2022; Huang et al., 2023a).
Learning- based approaches have emerged as the dominant paradigm due to their powerful representation capabilities to encode the historical motion profiles of agents and the topological and semantic information of environments. In general, data-driven trajectory prediction can be seen as imitation learning from human drivers, i.e., neural networks aim at learning human- like driving behaviors or strategies by leveraging large amount recorded driving data as expert demonstrations. This typical robotic task can be approached mainly in two ways: behavior cloning (BC) and inverse reinforcement learning (IRL). Most advanced methods in motion forecasting predominantly employ the BC frame- work, which involves directly learning the distribution of trajectories from real-world datasets in a supervised manner. In contrast, the IRL architecture models the agent's 's behavior as a sequential decision decision-making process (Osa et al., 2018) and aims to infer the underlying reward function that con-
1. Introduction
Trajectory prediction for surrounding traffic participants plays pivotal role in modern autonomous driving systems, serving as crucial bridging module that connects upstream perception to downstream planning. Accurately anticipating the future behaviors of nearby agents is paramount to ensure
Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, China Voyager Research, Didi Chuxing. China "Zhuoyu Technology Co., Ltd., Shenzhen, China. Correspondence Shaoshuai Shi <shaoshuaics@e @aaissg@@@@aooooo gmail.com>.
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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GolRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction
sidered the most parsimonious and robust representation of the expert demonstrations (Ng & Russell, 2000).
as it necessitates a forward RL-style procedure in the in- ner loop (Ho & Ermon, 2016), making it challenging to scale up for larger state spaces. To mitigate this concern, we propose a hierarchical architecture that generates pre- dicted trajectories in a coarse-to-fine manner. Concretely, on the initial coarse scale, we generate multimodal trajec- tories conditioned on diverse paths or policies drawn from the learned reward distribution using Markov chain Monte Carlo (MCMC) sampling (Hastings, 1970). Additionally, our approach employs a Bézier curve-based parameteri- zation method that recurrently forecasts control points to represent the trajectory, ensuring numerical stability and smoothness. Furthermore, the MCMMCinduccd distribution is also fused to constitute the final hybrid probability for each modality, thereby enhancing prediction confidence. On the subsequent fine scale, we introduce trajectory refine- ment module that leverages both observed and predicted trajectories to retrieve fine-grained local context features, enabling more consistent and precise trajectory forecasts.
Despite achieving impressive performance in trajectory pre- diction benchmarks, current supervised models still face challenges concerning generalization or domain adaptation, whereas IRL offers a promising pathway to alleviate them. Specifically, when the situation encountered significantly -itor--distribution of training demonstrations (referred as covariate shift in BC (Chen et al., 2023; Yao et al., 2024)), there is risk of severe compounding error, yielding unrea- sonable forecasts. For instance, consider a driving scenario where a temporary roadblock is set up in an intersection, causing a previously free space to become an undrivable area, as depicted in Figure Existing supervised models can hardly react to such changes, resulting in unaltered pre- dictions since the novel scene substantially differs from the training time. Besides, few approaches adequately consider drivable information while also having the capacity to effec- tively utilize this essential attribute, as the planning module does. However, IRL can handle such situations in principle, due to its reward-driven paradigm and learning from inter- action property rather than directly fitting data distributions (see Figure 5). Another critical concern associated with the supervised manner is the modality collapse issue. As only one -ruth future trajectory is provided as supervision, the predictor has to generate diverse plausible predictions via learning one-to-man mappings (Ridel et al., 2020). In contrast, the IRL framework holds the potential to address uncertainty by integrating the maximum entropy (MaxEnt) principle (Ziebart et al., 2008). The MaxEnt IRI. approach intends to acquire the reward distribution with the highest entropy (Kretzschmarr et al., 2016), which can better capture the intrinsic multimodality of demonstrations. Moreover, the learned reward, as an interpretable intermediate repre- sentation (Zeng et al., 2019), can also benefit downstream decision-makinn and behavior planning in highly complex and interactive scenarios (Huang et al., 2023b).
Overall, the main contributions of this paper can be sum- marized as follows: (1) We present a novel Graph-oriented Inverse Reinforcement Learning (GoIRL) framework for the multimodal trajectory prediction task, which, to the best of our knowledge, is the first to integrate the MaxEnt IRL paradigm with vectorized context representation through our proposed feature adaptor. (2) We introduce a hierarchical parameterized trajectory generator for improving prediction accuracy and an MCMC-augmented probability fusion for boosting prediction confidence. (3) Our approach achieves -tate-of-the-art performance on two large-scale motion fore- casting benchmarks, namely Argoverse (Chang et al., 2019) and nuScenes (Caesar et al., 2020). Further, it demonstrates superior generalization abilities compared to existing super- vised models in handling drivable area changes.
2. Related Work
2.1. Scene Context Representation
In light of its superior properties, the MaxEnt IRL frame- work has garnered significant attention in recent research (Finn et al., 2016a; Zhang et al., 2018). However, most tra- ditional IRL algorithms typically operate efficiently in grid- like environments, which prompts existing work to adopt rasterized context representations, rendering scene elements into bird's seed---ee--vew (BEV) images as input (Kitani al., 2012; Guo et al., 2022). Consequently, the performance of IRI-based predictors is hampered by scene information loss and inefficient feature extraction when compared to current supervised models with vectorized representations (Gao et al., 2020; Liang et al., 2020). To bridge this gap, we present a feature adaptor capable of aggregating lane-graph features into grid space, thereby empowering IRL-based predictors with vectorized context information. Another bottleneck lies in the computational expense of running IRL,
Scene context, including high-definition (HD) maps, of- fers valuable information that significantly contributes to trajectory prediction. Early works often rasterize the envi- ronment into BEV image, with distinct colors representing different types of input information. Scene features are subsequently extracted using convolutional neural networks (CNNs) and pooling layers (Cui et al., 2019). Neverthe- less, these rasterization-based methods have limitations in capturing rangerange spatiotemporal relationships owing to the lack of detailed geometric information from road maps (Nayakanti et al., 2022). Therefore, a more effective and powerful alternative, known as vectorized (Gao et al., 2020) or graph-based (Liang et al., 2020) representation, is then proposed, which can provide abundant geometric and se- mantic information, such as map topology, lane connectivity.
2

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GolRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction
and correlation relationships among neighborhood agents. Building upon these vectorized data, graph neural networks (GNNs) and Transformer-based architectures have been ex- tensively explored for feature extraction and fusion (Zeng et al., 2021; Zhou et al., 2023). This paradigm has gained increasing popularity in current prediction models due to its remarkable enhancement to overall prediction performance. Consequently, in our framework, we also adopt the prevalent vectorized representation encode the scene context and employ graph-based models to extract lane-graph features.
applied infer both future destinations and routes in real- world navigation tasks (Ziebart al., 2008). Nevertheless, previous IRL-based predictors have primarily been designed for path forecasting (Ziebart et al., 2009), neglecting the consideration of time profiles. To overcome this disparity, recent studies integrate kinematics and environmental con- text into the IRL scheme (Zhang et al., 2018), presenting a plans-to-trajectorii module that can generate continuous trajectories conditioned grid-based state sequences sam- pled from the reward distribution (Deo & Trivedi, 2020; Guo et al., 2022). However, existing IRI- predictors solely utilize rasterized BEV features as input, which limits their prediction performance. In contrast, our work introduces a novel feature adaptor designed to incorporate lane-graph fea- tures into the MaxEnt IRL framework, ultimately enhancing prediction accuracy.
2.2. Multimodal Trajectory Prediction
Multimodal trajectory prediction necessitates generating diverse, socially acceptable, and interpretable future tra- jectories accompanied by corresponding confidence scores (Huang et al., 2023a). One practical approach is to utilize stochastic techniques, such as generative adversarial net- work (GAN) (Gupta et al., 2018) or conditional variational autoencoder (CVAE) (Ivanovic et al.. 2020), to generate mul- tiple possible forecasts. However, sampling from a latent distribution is uncontrollable during inference, prompting recent efforts to focus on anchor-based methods instead. Predefined anchors, including goal points (Gu et al., 2021), reference lanes (Song et al., 2021), or candidate paths (Af- shar et al., 2024), can act as mode-specific priors to facilitate forecasting diversity. Nevertheless, the accuracy of predic- tions heavily relies on the quality of these anchors. By contrast, our work leverages MaxEnt IRL to infer the in- trinsic multimodal distribution of rewards by maximizing entropy. Multiple plausible policies or plans can then be sampled from the learned reward distribution, generating diverse trajectories. Furthermore, the probability of each modality is commonly obtained through classification with hard assignments using displacement regression (Ye al., 2021). Yet, we contend that the confidence scores obtained in this manner are inadequate to characterize uncertainty comprehensively and thus propose to augment the confi- dence scores by fusing the MCMC-induced distribution.
3. Methodology
3.1. Problem Formulation
The multimodal trajectory prediction task entails generating multiple plausible future trajectories for the target agent, each accompanied by corresponding probabilities condi- tioned on the scene context. More specifically, considering the driving context C = {x, M,M), which consists of the tracking positions of the target agent X [x: [1- To] and its observed neighboring agents O = [o 10-t,,1,.... On) spanning the past t, timestamps, as well as the relevant map information M, the motion predictor aims to infer the probability distribution of future forecasts P()CC), where
) lu....., Út,] represents the predicted future trajectory of the target agent over the future I timestamps.
To tackle trajectory prediction using IRL-based methods, we decompose the entire task into two conceptual stages: policy inference and trajectory generation. The scene context C is first aggregated into a coarse 2-D grid space. Then, the IRL framework is characterized as a finite Markov decision process (MDP) with a fixed horizon H. which is defined as a four-tuple (S, AS, T, R). Herein, S represents set of states comprising all grid cells, while A represents a set of actions consisting of nine discrete movements, including eight adjacent and diagonal directions, along with one end action for the early rollout termination. T S x A - S denotes the deterministic transition model and R denotes re- ward function which is initially unknown. Next, we leverage stationary policy (a]s)) derived from the learned reward distribution to specify probabilistic mapping from a state E S to a particular action E A. Ultimately, the tar- get agent makes forecasts conditioned on grid- based plans sampled from the optimal policy π², where each plan is re- ferred to as a sequence of states given by i = = .xx]..,,,]] Consequently, the multimodal future trajectory distribution P()(C) can be decomposed by conditioning on plans and
2.3. Inverse Reinforcement Learning
Inverse Reinforcement Learning (IRL), a prominent branch of imitation learning, has been extensively investigated in the domains of robotic manipulation (Finn et al., 2016b), navigation (Fu et al., 2018), and control (Yu et al., 2019; Osa et al., 2018). It aims to recover the underlying reward distri- bution from expert demonstrations, enabling the derivation of policies consistent with human behaviors. Supposing that surrounding agents are mostly rational and thus can be mod- eled as optimal or suboptimal planners, the IRL approach becomes a powerful tool for motion forecasting, function- ing as a planning-based predictor. In order to reason about uncertainty in decision sequences, a probabilistic approach known as MaxEnt IRL has been proposed and successfully
3

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GolRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction
Drivoiole Encoder
Syme
Cueorea
Lane Segment Encoder & Fusion
Feature Adoptor
MaxEnt IRL
Béaier Curve- Based Trajectory Proposol Decoder
Refinement Module
Plan
Feature Encoder
Driving Context Input
Policy Inference
Trajectory Generation
Multimodal Predictions
Figure 2. Overview of GolRI, illustrating the generation of multimodal trajectory predictions for the target agent (depicted in blue).
then marginalizing over them:
ture for encoding the driving context. Here, we take both lane segments and drivable areas into account because the drivable areas also offer valuable traffic information. Firstly, we construct lane graph based on the vectorized map data, where each lane node represents a polyline segment and provides essential geometric and semantic attributes, includ- ing the types of connections. Then, the dilated LaneConv operator proposed in LaneGCN (Liang et al., 2020) is ap- plied to extract the lane-graph features. Subsequently, we uniformly sample nodes within drivable areas and build an interconnected spatiotemporal occupancy graph. Afterward, the node features of the drivable area are updated using PointNet-lik: network (Qi et al., 2017) with dilated connec- tions. In addition, we leverage a 1-D CNN with a feature pyramid network (FPN) (Lin et al., 2017) to encode the kinematic profiles of all agents in the scene, encompassing historical positions, velocities, time intervals, etc. Finally, stack of fusion modules with graph attention layers is employed to capture the interactions among the aforemen- tioned vectorized embedding features and update the final fused context features. More details of the encoding process can be found in Appendix A.1.
P(IC)= E P(
(1)
FES(C)
where S(C) denotes the space of plausible plans based on the driving context, which is derived from the policy inference.
3.2. Framework Overview
An overview of our proposed framework is presented in Fig- ure 2, which illustrates a two-stage architecture involving policy inference and trajectory generation. In the first stage, we encode the driving context in a vectorized manner and employ a graph- approach to extract scene features. The lane-graph features are then aggregated into grid space using the proposed feature adaptor and further compressed through CNNs to reduce the state-space dimension. Af- terward, the grid-based MaxEnt IRL algorithm is utilized to infer the reward distribution, thereby obtaining the opti- mal policy that can be sampled to induce multiple plausible plans or traversals over the 2-D grid. In the second stage, we introduce a hierarchical structure for generating multi- modal future trajectories conditioned on the sampled plans and multiscale scene embedding features. Concretely, we parameterize predicted trajectories using Bézier curves and recurrently produce control points to represent continuous trajectories as initial proposals. Subsequently, a refinement module designed to generate location offsets for each clustered proposal by retrieving ane-ggrined local context embedding features via the complete trajectory, which com- prises both the predicted proposal and past observation, in order to facilitate temporal consistency and spatial accuracy.
As efficient IRL-based methods typically rely on image- or grid-shaped features as input, devise feature adaptor to aggregate the graph-base based context fea- tures into grid space. To achieve this, we construct grid map centered around the target agent, with each grid cell uniformly spaced and aligned with drivable nodes. The fused context features within the drivable areas are then assigned to their corresponding cells based on physical loca- tions, while the undrivable cells are padded with zeros. This operation successfully transforms the vectorized features into grid-shaped driving context features, denoted Cfines which can be seamlessly adapted to the IRL framework. Moreover, considering the high-resolution grid space leads to the IRL process being extremely time-consuming, we employ CNNs with strides to downsample the spatial dimen- sion of the original feature map, effectively alleviating the computational burden without losing essential information. Consequently, the coarse -rainned context features denoted
Feature Adaptor.
3.3. Graph-Oriented Context Encoder
Considering context rasterization suffers from information loss and inefficient feature extraction, we employ graph- oriented context encoder to aggregate scene features in a vectorized manner, enabling better capture of complicated topology connectivity and long-range interactions. Specifi- cally, we adopt an agent-centric double- layered graph struc-

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GolRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction
Algorithm 1 Approximate Value Iteration
((())
Input: S, S,A,TRR
((a)
BiGRU
Output: T(als)
GRUCell w/ Att.
GRUGell
GRUGell Att.
1: @(s,a) = 0, (()) -0, Vs EsE
I(s
2: for = 1 N do
MIP
Agent Feature
3: V(5) < R()), 8 Sgont
Rio
4: Q a) = (s) + V('),, s' = a)
MLP
5: V(s) = log
exp (Q(s,a))
Canura Con (4
MLP
MLP
6: end for
8
MLP.
7: m[ass) exp (Q(s,a) V())
n- order
Bézier Curve
Conerse are further extracted using 1 CNNs to yield the reward distribution, denoted R. Overall, the reward can be regarded as nonlinear combination of the driving context throughout the entire encoding process.
Figure 3. Structure of Bézier curve-based trajectory proposal de- coder for each sampled plan.
3.4. MaxEnt IRL-Based Policy Generator
After modeling the reward function neural network, aim infer the optimal policy that can generate multiple plausible plans within the grid. Following the MaxEnt IRL framework (Ziebart et al., 2008), the probability of state sequence (or plan) is proportional to the exponential of the total reward accumulated over the planning horizon H::
state set Sgaat is unknown in the trajectory prediction task, the terminal state distribution is also inferred by the neural networks. Upon convergence of the reward distribution, we can acquire the optimal MaxEnt policy π², which enables the generation of multiple plans over the 2-D grid, serving as trajectory generation priors.
1 P(r) z
exp (R(T)) exp Σ R(s))
(2)
3.5. Hierarchical Multimodal Trajectory Decoder
Based on the converged reward model R and the optimal MaxEnt policy x², along with multiscale driving context features Comase and Cfines we present a hierarchical trajec- tory decoder to generate K multimodal predictions and their corresponding probabilities in a coarse-to carse-to-fine to-fine manner.
where r = [s1,..., .a.....,./ sh] represents any given plan and Z denotes the partition function. Further, we translate the continuous-vally future trajectories from the dataset into discrete state sequences using uniform quantization tech- nique with specific resolution, constituting set of demon- strations denoted as D (Ti,..., T }. The objective is to maximize the log-like ligliike of the demonstration data Lo under the MaxEnt distribution. This optimization prob- lem can be solved using grad approaches, and the gradient is given by
On the initial coarse scale, we generate multiple plausible trajectory proposals conditioned on the sampled plans and associated coarse -oasse-graned context features, as illustrated in Figure 3. Specifically, we first employ the learned Max- Ent policy to induce plans over the 2-D grid cells using the Markov chain Monte Carlo (MCMC) sampling strategy. Each plan is then utilized extract features from the coarse- grained context feature map Ceoarse and the reward map R along the state sequence. For each state (or grid) s; within plan we adopt simple multilayer perceptrons (MLPs) to encode its local context features Ccourse (s::), (s:), reward R(s:), and grid location coordinates I(s;), respectively, and con- catenate them as the state feature embedding e(s;), i.c.
vLp (ND BljJ) VR,
(3)
where juD represents the average state visitation frequen- cies (SVFs) from the demonstrations and [[[μ] refers to the expected SVFs under the policy (Wulfmeier et al., 2017), which can be derived via a forward RL process given the current reward distribution. Here, we leverage the approxi- mate value iteration algorithm (detailed in Algorithm 1) to obtain the MaxEnt policy т (a]ss) over N update steps with the following expression:
e(st) (Croaree (s.)) = f2(((s:))
E fa(I(s:))) (5)
where il represents the concatenation operator, and fz.j
π (a|s)) exp (Q(s.a) a) V(s)),
(4)
1, 2, 3 denotes a simple MLP block. The state feature em- beddings e(s;) over the entire plan T are further aggregated via bidirectional gated recurrent unit (BiGRU) encoder, yielding the plan feature E(T). Next, instead of directly
where Qs,, a) represents the action-value function and (s) refers to the state-value function. Note that since the goal
5

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GolRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction
predicting the future trajectory positions, we employ an π- th order Bézier curve to represent continuous trajectories. Herein, we adopt GRU decoder with the soft attention mechanism (Bahdanau et al., 2015) to recurrently generate n + 1 control points:
previous updated agent features, as well as the location embeddings obtained by encoding the complete trajectory locations through an MLP block. The fused features are fur- ther fed into MLP blocks with residual connections, which comprises a regression head for producing the predicted trajectory offsets, denoted Aý;, and a classification head (6) followed by softmax function for generating the probabili- ties, denoted Pals-
P: = (((s+1)s;
h441 = ((Att(E(7))ha),
(7)
Eventually, the i-th predicted trajectory 5 can be derived by summing the trajectory proposal and offset:
where pr, = O,...,7,, n, is the control point for the Bézier curve, h2 is the hidden state of the GRU, and the initial one hg is the updated target agent feature obtained by aggregat- ing fused context features and interactions among agents through the agent fusion module. yp denotes an MLP with single hidden layer, G represents the GRU cell, and tt denotes the soft attention module. Once the control points are generated, the continuous trajectory, denoted B(t), can be obtained using the following expression:
J = St + +A).
(10)
Its corresponding fusion probability takes a hybrid form:
Pata Pata()'))Pomm (5xt)
pO = Prt Pomooo Pmmmmmmmmmm (St)
(1)
K Σ
B(t)= = Σ (t.tt)pp OstsI, 1=0
(8)
3.6. Learning
Given that our proposed framework consists of two stages, the training process necessitates a decomposition into two phases. In the initial MaxEnt IRL. stage, our objective is to maximize the log-likelihood LD through stochastic gradient descent to derive the reward model and optimal policy, as explained in Section 3.4. In the second trajectory gener- ation stage, the overall learning objective is composed of both regression loss and classification loss. Specifically, for regression, we apply the Huber loss to the predicted trajectory proposal Chegg the refined trajectory Zreg. and its corresponding goal point LG The winner-takes-all (WTA) training strategy is employed to mitigate the modality col- lapse issue, which only considers the best candidate with the minimum displacement error in comparison to the ground truth. As for classification, we adopt the Hinge loss Let, to distinguish the positive modality from the others, following the approach outlined in (Liang et al., 2020). The total loss L in the second training stage can be expressed as follows:
where (t) (11 -) 0,..., n, is the n-
degree Bernstein basis polynomial, and (9) M[n i)! de-
notes the binomial coefficient. In practice, for given times-
tamp la, ta E 21, (1). the position of the predicted trajectory proposal J. can be determined by substituting with f,:
0. = 14
bin
(+) pi.
(9)
1=0
Considering that sampling only K plans is often inefficient and redundant, as a small number of samples tend to produce similar outputs, we oversample L (L >> K) plans in parallel, thereby inducing L continuous valued trajectories to better capture the trajectory distribution. Subsequently, we apply the K-means clustering method to derive K possible future trajectories from the set of L candidates. Moreover, we determine the probabilities by calculating the proportion of trajectories associated with each clustered modality, denoted P Pmemee which can reflect the statistical property of MCMC sampling from the MaxEnt policy.
C C= c + aaC. + 3C + Y
(12)
where a, 3, and are hyperparameters for balancing each loss component. In practice, we set a = B = 1 and y = 3. More details can be found in Appendix A.2.
On the second fine scale, we generate trajectory offsets to refine the K initial trajectory proposals in conjunction with fine-grained local context features Cfine- Concretely, we first combine past observations and predicated proposals together to form the complete trajectory for the target agent, i.e., [X, J1 l,..., K, where 5 denotes the i-th pre- dicted trajectory proposal. For each complete trajectory, we gather its nearby fine ime-grained context features. These embeddings are then aggregated along the entire trajectory using global average pooling and concatenated with the
4. Experiments and Results
4.1. Experiment Setup
Real-World Datasets. We train and evaluate the pro- posed approach on two large-scale public motion forecast- ing datasets: Argoverse (Chang et al., 2019) and nuScenes (Caesar et al., 2020). Both datasets provide trajectory se- quences collected from real-worke urban driving scenarios,
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GolRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction
along with HD maps that encompass rich geometric and semantic information. Specifically, the Argoverse dataset comprises 205,942 training, 39,472 validation, and 78,143 testing sequences. Each sequence spans 5 seconds and is sampled at 10 Hz. The task involves forecasting the subsequent 3-second trajectories based on the preceding 2 seconds of observations. As for the nuScenes dataset, it contains 38,186 training. 8,560 validation, and 9,041 testing sequences. Each sequence is 8 seconds long and sampled at 2 Hz. The goal is to predict the future 6-second trajectories given the past 2 seconds of observations.
Table I. Single-model results on the Argoverse motion forecasting
benchmark, ranked by the official metric brier mier-....DD..
Method
Brier score
minFDE,
minADE,
MRa
minFiEE
LaneRCNN (Zeng et al., 2021)
2.1470
0.6944
1.4526
0.9038
0.1232
LaneGCN (Liang et al., 2020)
2,0585
0.6945
1.3640
0.8679
0.1634
DSP (Zhang al., 2022)
1.8584
0.6398
1.2186
0.8194
0.1303
HeterrGCCN (Gao et al., 2023)
1,8399
0.6521
1.1878
0.8173
0.1236
GolRL (Ours)
1.7957
0.6232
1.1725
0.8087
0.1204
Table 2. Ensemble-model results on the Argoverse motion fore- casting benchmark, ranked by the official metric brier- minFDEs.
Evaluation Metrics We evaluate the performance of multi- modal trajectory prediction using the widely accepted met- rics, including miss rate (MRx). minimum average displace- ment error (minADER), minimum final displacement error (minFDEx), and the Brier minimum final displacement er- ror (brier-minFDExg) specific to the Argoverse benchmark. Concretely, the MR measures the proportion of scenarios where none of the K predicted endpoints fall within a 2.0- meter range of the ground truth. The minADE calculates the average pointwise lg distance between the best fore- cast among the K candidates and the ground truth, while the minFDEx solely focuses on the endpoint error. Fur- thermore, the brier-minFDEx incorporates prediction confi- dence by adding the Brier score (1.0- P)² to minFDE where P corresponds to the probability of the best forecast.
Method
brier- minFDE,
Brier spord
minFDEs
minADFs
MR.
MuliPathe+ (Varadarajan et al., 2022)
1.7932
0.5788
1.2144
0.7897
0.1324
HeterGGNN (Cian er al., 2023)
1,7512
0.5910
1.1602
0.78%)
0.1168
SIMPL (Zhang 2024)
1.7469
0.5924
1,1545
0.7093
0.1165
Wayfomerr (Nayakaati al., 2022)
1.7408
1.1616
0.7676
0.1186
GolRL (Ouss)
1.6947
0.5684
1.1263
0.7828
0.1102
Table 3. Quantitative results on the nuScenes prediction bench- mark, sorted by the official ranking metric minADE,.
Method
minADE;
minADE
minFDE;
MR;
MR
P2T (Deo & Trivedi, 2020)
1.45
1.16
10.5
0.64
0.46
PGP (Dea 2021)
1.27
0.94
7.17
0.52
0.34
MacFormer (Feng et al., 2023)
1.21
0.89
7.50
0.57
0.33
Goal-LBP (Yao et al., 2023)
1.02
0,93
9.20
0.32
0.27
GolRI (Ours)
0.86
0.75
6.53
0.21
Implementation Details. We employ the target-centric co- ordinate system, where all context instances and sequences are normalized to the current state of the target agent through translation and rotation operations. Note that augmen- tation techniques are applied in our method. Moreover, the spatial dimension of the grid space is initially defined as 100 x 100 and then downsampled to 25 x 25 for the MDP. The planning horizon H is configured as 25. Addi- tionally, during the training phase, we set the degree of the Bézier curve n = 5, the oversample number = 600, and the mode number K = 6 for Argoverse and K 10 for nuScenes. The first-stage model size amounts to 2.79M parameters, while the second-stage model consists of 0.85M parameters. We train our model on eight GPUs using the AdamW optimizer with a batch size of 256.
framework against several representative supervised mod- els with graph-based context encoders. It can be seen that our proposed method achieves the best results across all metrics. In particular, GoIRL surpasses the bascline model DSP (Zhang et al., 2022) by a large margin, highlighting the effectiveness of the IRL architecture in enhancing trajectory predictions.
Furthermore, we adopt an ensemble strategy (Zhang et al., 2024) to boost prediction performance, enabling a com- prehensive comparison against other supervised ensemble methods. As shown in Table 2, GoIRL continues to demon- strate highly competitive performance compared state- of-the-art supervised models like the strong baseline Way- former (Nayakanti et al., 2022). We also report the results on the nuScenes prediction leaderboard in Table 3 to ex- hibit the long-term prediction performance of our proposed framework. As presented, GolRL achieves top-ranked per- formance on this benchmark, remarkably outperforming all other approaches across all evaluation metries. including the IRL-based baseline method P2T (Deo & Trivedi, 2020) that represents the driving context in rasterized manner. This outcome illustrates that by leveraging the feature adaptor to effectively incorporate the lane-graph features, we can significantly improve the upper bound of performance for IRL-based predictors. This advancement holds great poten- tial to empower multimodal trajectory prediction tasks.
4.2. Quantitative Results
Comparison with State-of-the-Art. We compare our ap- proach with state-of-the-arr methods on both Argoverse and nuScenes motion forecasting benchmarks. Table shows quantitative results of the single-model performance on the Argoverse test split. The official ranking metric is shaded in gray, and the best results are indicated in bold. All met- rics follow a lower-the-better criterion. To the best of our knowledge, no IRL-based predictor is publicly available on the Argoverse leaderboard. Thus, we compare our GoIRL
7

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GolRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction
Table 4. Ablation studies on the Argoverse test split.
Goand Fradetiain
Refine
Bezier curve
Recurrent stralegy
Poemn
brier- minFDE,
Brier score
minFDE,
1,8280
0.6468
1.1812
x
1.7993
0,6242
1.1751
x
1,8000
0.6236
1.1764
1.8099
0.6310
1.1729
1.7957
0.6232
1.1725
A Ablation Study. We conduct thorough ablation studies on
the Argoverse test split investigate the fuuctioonality of
several key components of the trajectory decoder. Each of them is ablated from the complete pipeline to quantify its individual impact on the final performance, as presented in Table 4. The results reveal that the refinement module makes a substantial contribution to prediction accuracy, un- derscoring that the hierarchical architecture with effective aggregation of fine-grained features can notably improve location precision. In addition, both the Bézier curve-based trajectory parameterization and the recurrent strategy for point generation bring benefits to distance-aware metrics while also ensuring kinematic feasibility and temporal con- sistency. Furthermore, the comparison of the Brier score metric clearly demonstrates that the probability fusion with the MCMC-induse distribution Pemme leads to remarkable enhancements the predictive confidence score, thereby emphasizing its efficacy in capturing the multimodal distri- bution of future trajectories. In summary, all components within our proposed framework play vital roles in attaining superior prediction performance.
Figure 4. Visualizations of GolRI. on the Argoverse validation set. The historical trajectory, ground-truth fuuture trajectory, and multimodal predictions are depicted in red, magenta, and green. respectively. Other traffic participants have been excluded to em- phasize the predictions for the target agent.
Chanatane
4.3. Qualitative Results
We showcase some visualizations of our proposed method under diverse traffic scenarios from the Argoverse validation set, as depicted in Figure From the qualitative results, it is evident that our approach successfully anticipates accurate and feasible multimodal future trajectories that conform to the scene layout. Additionally, apply our model to the Argoverse tracking dataset without any further fine-tuning, as detailed in Appendix C.I. The consecutive trajectory prediction results are available in the supplementary video'.
(a) GolRL
(b) DSP
Figure 5. Qualitative comparisons between GoIRL (left) and DSP (right) in handling drivable area changes. The original predictions are depicted blue, while the updated trajectories are green. The undrivable area is indicated with a "STOP" sign symbolizing the transformed region.
changes due to the lack of consideration for drivable infor- mation, resulting in irrational predictions or even potential crashes. Hence, we compare our approach against DSP (Zhang et al., 2022), which, to the best of our knowledge, is the only supervised model that incorporates drivable in- formation. As shown in Figure 5(a), GoIRL can effectively adapt to changes in the environment and generate reason- able predictions, thanks to the inherent interaction learning property of the IRL paradigm. In contrast, Figure 5(b) show- cases that the DSP model fails to respond appropriately. thereby highlighting the superior generalization ability of IRL-based predictors in addressing such domain bias issues. More qualitative results can be found in Appendix C.2.
IRL-based v.s. BC-based predictor. We conduct an in- vestigation into the generalization and domain adaptation abilities of our GoIRL framework with respect the driv- able area attribute. To achieve this, we modify the drivable attribute of traffic scenario within the original dataset, transforming a previously designated free space into an un- drivable area, as demonstrated in Figure 5. Our primary objective is to evaluate the capability of predictors in han- dling such distribution-shifting cases. Unfortunately, exist- ing methods often fall short of adequately reacting to such
8

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GolRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction
5. Conclusion
Caesar, H., Bankiti, V., Lang, A. H., Vora, S., Liong, V. E., Xu, Q. Krishnan, A., Pan, Y., Baldan, G., and Beijhom, O. nuscenes: A multimodal dataset for autonomous driving. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 11621-11631 2020.
In this paper, we introduce GolRL, a graph-oriented inverse reinforcement learning framework for multimodal trajec- tory prediction tasks. To the best of our knowledge, GoIRL is the first motion prediction scheme that integrates the MaxEnt IRL paradigm with graph-based context represen- tations through the proposed feature adaptor, facilitating effective scene feature extraction and aggregation. More- over, the hierarchical parameterized trajectory generator remarkably enhances prediction accuracy, while the MCMC- augmented probability fusion strategy amplifies prediction confidence. Experimental results large-scale motion forecasting benchmarks demonstrate that GoIRL excels in generating scene-comee complaan multimodal future trajectories and outperforms the current state-of-the-an methods. The advantages of the IRL paradigm also empower GoIRL with exceptional generalization and domain adaptation capabili- ties, allowing it to effectively address distribution-shiftin challenges, such as drivable area changes, when compared to existing supervised models. Our work underscores the effectiveness of IRL-based motion predictors and provides a promising baseline for further investigations. Future work will concentrate on extending the IRI. paradigm to encom- pass joint multi-agent trajectory forecasting.
Chang, M.-F., Lambert, J., Sangkloy, P., Singh, J., Bak, S., Hartnett, A., Wang, D., Carr, P., Lucey, S., Ramanan, D., et al. Argoverse: 3d tracking and forecasting with rich maps. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 8748- 7757,2019.
Chen, L.,, Wu, P., Chitta, K., Jaeger, B., Geiger, A., and Li, H. End-to-end autonomous driving: Challenges and frontiers. arXiv, 2330616927,, 2023.
Cui, H., Radosavljevic, V., Chou, F.-C., Lin, T.-H., Nguyen, T., Huang, T.-K., Schneider, J., and Djuric, N. Mul- timodal trajectory predictions for autonomous driving using deep convolutional networks. In 2019 international conference on robotics and automation (icra), pp. 2090- 2096. IEEE, 2019.
Deo, N. and Trivedi, M. M. Trajectory forecasts in unknown environments conditioned on grid-based plans. arXiv preprint arXiv:2001.00735, 2020.
Acknowledgment
Deo, N., Wolff, E., and Beijbom, O. Multimodal trajec- tory prediction conditioned on lane- ann-graph traversals. In Conference on Robot Learning, pp. 203 2021.
This work was supported in part by the Hong Kong Ph.D. Fellowship Scheme, and in part by the HKUST-DJI Joint Innovation Laboratory. The authors thank Xiaogang Jia, Xu Liu, Zhaojin Huang, Wenchao Ding, and Haoran Song for their insightful discussions.
Feng, C.,, Zhou, H., Lin, H., Zhang. Z., Xu, Z.,, Zhang, C., Zhou, B., and Shen, S. Macformer: Map-agent coupled transformer for real-time and robust trajectory prediction. IEEE Robotics and Automation Letters, 2023.
Impact Statement
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.
Finn, C., Christiano, P., Abbeel, P., and Levine, S. A con- nection between generative adversarial networks, inverse reinforcement learning, and energy-based models. arXiv preprint 1rXiv: 2016a.
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GolRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction
A. Additional Implementation Details
In this section, we provide a more detailed description of the context encoder, feature fusion, and adaptation, along with the specific formulations of the various training losses.
L2D
D2D
D2L
L2L
A.1. Graph-Oriented Context Encoder
A2L
Our graph-oriented context encoder follows a structure simi- lar to the one used in DSP (Zhang et al., 2022), which adopts an agent-centric, double-layered, graph-based representa- tion. This encoder consists of three components: an agent feature encoder, a lane segment encoder, and drivable area encoder.
L2A
A2A
Figure 6. Information flow of agent-map feature fusion.
Agent Feature Encoder. Given the observed past times- tamps tp. we define the agent trackings as A RVV, xt, F2, where N₂ is the number of agents in the scene, and F% encompasses kinematic attributes such as positions, veloc- ities, time intervals, and binary masks. To be specific, the agents include the target agent X' and surrounding agents O. Next, We utilize 1-D CNN with a feature pyramid network (FPN), as implemented in (Liang et al., 2020), to capture multi-scale features. This results in the agent feature CA E NR xF, where Fa 128 the number of feature channels.
pling drivable nodes centered around the target agent within a I 100-meter range and a resolution of meter. These nodes are denoted Va E IR RRNax2, where Na is the number of driv- able nodes. We use eight-neighbor dilated connections to model relationships between the drivable nodes. The fea- tures encoded using a PointNet-like architecture, termed Poi ntDA. Specifically, we map surrounding node features to the target node using an MLP block, followed by max- pooling to extract global features. These global features are then concatenated with the target node feature and passed through another MIP block to fuse the features. The final drivable area features are denoted as CD E R with Fa 32 being the number of feature channels.
Lane Segment Encoder. Given the map information M, we define the lane node matrix V, E RNNx2,, where Ni is the number of lane segments, and each entry represents the midpoint between two neighboring nodes along the lane centerline. The connections between these nodes include the predecessor, successor, left, and right neighbors, which are captured by four adjacency matrices (T, hie (pre, suc, left, right]. where each Y; E I N For each lane node 2s E Vi, we define its node feature uy E U as:
Feature Fusion. To capture agent-map interactions, we perform feature fusion on the agent features CA, lane seg- ment features Cr,, and drivable area features Cp. following the approach in (Liang et al., 2020; Zhang et al., 2022). We employ graph attention layers (Vaswani et al., 2017: Liang et al., 2020) to fuse features across different node types: agent-to-lane (A2L), lane-to-agent (L2A), drivable- to-lane (D2L), lane-to-drivable (L2D), and agent-to-aan to-agent (A2A). Additionally, we use the LaneConv operator for lane-to-lane (I.2I.), and DiiD for drivable-to-drivable (D2D), All attention layers are set to 128 feature channels. The information flow for all fusion processes shown in Figure 6.
w/ (Av:) + (2(11,,
(13)
where 11 and ui are MLP blocks, and Au; denotes the displacement of neighboring lane nodes. The resulting node feature matrix is U E I NI where Fi 128 is the number of lane feature channels. We then apply the multi- scale dilated LaneCorv operator, as proposed in (Liang al., 2020), to aggregate the topology features across larger lane graph:
To integrate the MaxEnt IRL framework with vectorized features, we design a feature adaptor that transforms the lane-graph features into grid space. We con- struct a HG x We grid map centered around the target agent within a 50-meter range, uniformly sampling grid nodes at a resolution of 1.0 meter, which aligns with the drivable area graph. Thus, we have HG = WG = 50. For each grid node with physical coordinates (z,,, 9:). we assign the corresponding nearest drivable area features CD (2:,, vi) as its fused feature. For grid nodes whose distance to the nearest drivable node exceeds 1.0 meter, indicating they are undrivable, we pad their features with zeros. In this way, we complete the adaptation of the vectorized context features
Feature Adaptor.
C₁ = c.=I(r (M U
pre + suc
UO
sue)
(14)
+ Tofee UOieft Tright rightt + UOo.
where 21,,,4,8, 32) represents the dilation sizes, and θ are the weight matrices associated with the i-th connection type. The resulting lane features are represented as Cr, E M...
Drivable Area Encoder. We construct the drivable area (DA) graph, as in (Zhang et al., 2022), by uniformly sam-
12

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GolRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction
into grid-based format, which can then be used in the subsequent MaxEnt IRL process.
Table 5. Results on the Argoverse motion forecasting henchmark.
Method
bries- minFFD,
Brier scone
minEDE
minADE,
MR,
A.2. Training Objectives
LancRCNN Zong al., 2021)
2.147
0.694
1.453
0,904
0.123
We detail the mathematical formulations of the training ob- jectives, including both regression and classification losses.
LaneGCN (Liang
2020)
2,059
0.695
1.364
0.163
AutoBot (Gingi ct 2022) 2022)
2.057
0.685
1.372
0.876
0.164
THOMAS (Gilles et 2022a)
1.974
1.439
0.104
GOHOME (Gilles ct al., 2022b)
1.983
0.533
1,450
0,943
0.105
Given K predicted trajectories Si = [u ........ Stt, for k = 1.2..... K, and the ground-truth future trajectory y/TT= = GT tory 'n' as the one with the minimum final displacement error relative to yGT.
HOME (Gilles 2011)
1.860
1.292
0.085
DSP (Zhang et 2022)
1.858
0.639
1.219
0.819
0.130
HIVT iZhou al. 2022)
1.842
1.169
0.127
1/2 GT ..... M/y J. we identify the positive trajec- . GT),
MuliPathh-1 (Varadarnjan et al. 2022)
1.793
0.579
1.214
0.790
0.132
GANet (Wang et al., 2023)
1.790
1.16]
0.118
HereroGCN (Giao et al., 2023)
1.751
0.591
1.160
0,789
0.117
SIMPL (Zhang et 2024)
1.747
1.155
0.117
Wayforeer (Nayakanti et al., 2022)
1.741
0.579
1.162
0,768
0.119
Regression Loss. The regression loss is calculated using the Huber loss. Taking the refined trajectory loss Cieg as example, it is defined as:
QCNet (Zhou al., 2023)
1.693
1,067
0.106
SEPT (Lan et al., 2023)
1.682
0.625
1,057
0.728
0.103
GolRL (Ours)
1.695
0.569
1.126
0.783
0.110
C. Additional Qualitative Results
GT 12). Greg = Huber yi
(15)
In this section, we provide additional consecutive trajectory prediction results, examples of generalization to drivable area changes, and some representative failure cases.
where || l12 represents the fz-norm, and the Huber loss function Huber(-) is the smooth E loss given by:
00.22²
if | < <I,
Huber(x)) = ||=||1 - 0.5 otherwise,
(16)
C.1. Consecutive Trajectory Prediction
Experimental Settings. To effectively demonstrate the prediction performance of our proposed GoIRL model, we directly apply it to the Argoverse tracking dataset (Chang et al., 2019) without any additional training. The experimen- tal settings are fully consistent with those of the Argoverse motion forecasting benchmark. For clarity and relevance, we filter the predictions to include only vehicles within a 50-meter radius of the ego agent and traveling at speeds above 2 m/s, excluding all others from the visualization. We predict six future trajectories for each vehicle, each associ- ated with probability score. To enhance the visual clarity in the demo video, multimodal trajectories are rendered with varying transparency based on their corresponding proba- bilities. Specifically, as shown in Figure 7, trajectories with lower probabilities are displayed with greater transparency, ensuring clean and intuitive visualization.
where || |12 denotes the l1 no-norm
In addition, for the trajectory proposal loss Creg we replace off with the trajectory proposal o Similarly, for the goal point loss Greg. only the final term Bi, is considered.
Classification Loss. The classification loss Lots is com- puted using the Hinge loss (max-margin loss) for binary classification. It is defined as:
Lets = K -
Σ (a - -Pets t 0), K
(17)
where 8 is the margin, and (Sat represents the proba- bility of trajectory DE for k = I,...,K. K.
B. Additional Quantitative Results
Snapshots in the Demo Video. In consecutive prediction scenarios, we expect the multimodality of predictions to be more evident initially; as the vehicle continues, its intent becomes clearer, leading to reduced diversity in predictions. For example, in straightforward scenarios where vehicles travel straight, the prediction with the highest probability should closely align with the ground truth, while alternative predictions capture slight variations in velocity or endpoint. Conversely, at intersections, significant multimodality typi- cally arises, capturing various potential maneuvers. Some snapshots showcasing these multimodal predictions are high- lighted in Figure 7. The visualizations indicate that GoIRL performs robustly in such consecutive predictions, under- scoring its effectiveness in practical applications. Additional
To comprchensively demonstrate the effectiivness of our GolRL in trajectory prediction, we provide several recent entries from the Argoverse leaderboard, as shown in Table 5, including both supervised and self-supervised models. Our GolRL achieves a competitive brier-minFDEs and a supe- rior Brier score relative to strong supervised baselines, such as those with more powerful scene encoders (Zhou et al., 2023) as well as recent sulf-super methods (Lan et al., 2023), highlighting both reliable predictions and strong overall performance. In summary, our approach employs a graph-bases based IRL framework that effectively mitigates co- variate shift while maintaining competitive performance on standard trajectory prediction benchmarks.
13

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GolRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction
Ego vehicle
Surrounding vehicles
-
Pedestrions
Predicted trajectories
Figure 7. Snapshots with multimodal predictions in the demo video.
Observations Grannd inch Prddictions
Ossevatices Guozni
prelettee Undi-abte anaa
observation.
Imperfect speed prediction.
Unpredictable changing.
Figure 8. Examples of generalization to changes in drivable areas. forecasted trajectories are in green, and the undrivable area is indicated with a "STOP" sign symbolizing the transformed region.
Figure 9. Visualizations of several representative failure cases.
qualitative results can be found in the latter half of the sup- plementary video² for further evaluation.
may underperform and point to potential directions for en- hancing the capability of the IRL-based trajectory predictor.
C.2. Generalization to Drivable Area Changes
D. Discussion: IRL v.s. BC
To further demonstrate GolRL's capability to address the covariate shift issues, we provide additional qualitative ex- amples, as shown in Figure 8. These case studies illustrate that our GolRL model can effectively adapt to changes in drivable areas and generate feasible forecasted trajectories, underscoring its strong generalization ability across diverse scenarios involving drivable area changes.
Inverse reinforcement learning (IRL) and behavior cloning (BC) are two primary paradigms in imitation learning (II.). While BC has been widely applied across various domains, including trajectory prediction, IRL offers several advan- tages for autonomous driving scenarios. Below, present intuitive comparison of these two approaches across three key aspects.
C.3. Failure Cases
Understanding Underlying Intentions. A fundamental difference between BC and IRL. lies their approach to learning behavior. BC directly replicates expert behavior using standard supervised learning without attempting to understand the reasons behind the actions. contrast, IRL aims infer the underlying objective reward function that explains the expert's behavior based on demonstrations (Osa et al., 2018). By understanding the motivations behind actions, IRL allows for better generalization to novel, unseen scenarios, enabling the agent to make decisions that align with the inferred intentions even different contexts.
We present several representative failure cases of our model. Figure 9() illustrates how poor observations of static slow-moving agents can negatively impact trajectory predic- tions. Figure 9(b) demonstrates that inaccuracies in speed prediction can affect longitudinal accuracy. Figure 9(c) high- lights a limitation where the model fails to anticipate a lane change in the absence of explicit cues. These examples offer some insights into the conditions under which our model
14

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GolRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction
Handling Distribution Shift (Covariate Shift). In II, the source domain comprises expert demonstrations, while the larget domain represents the learner's s reproductions. Since demonstration datasets cannot cover all possible situations, learners often encounter states that were not included in the dataset, leading to out-of-distribution or covariate shift sce- narios. BC, which heavily relies on patterns in the training data, struggles adapt to such unseen states. This limita- tion often results in compounding errors: small mistakes lead the agent into unfamiliar states, causing further enrors and eventual divergence. Conversely, IRI. learns reward function that suceinctly encapsulates the desired behavior. This reward function enables the agent to re-optimize its policy dynamically, reducing error accumulation, recover- ing from unfamiliar states, and adapting more effectively changes in the environment. Consequenty, IRL more robust in real-world driving conditions, where uncertainty and unpredictability are common, resulting in more reliable trajectory predictions.
Interpretability. BC operates as a black-box approach, of- fering little insight into why certain actions are taken. It also lacks the ability inherently account for constraints unless they are explicitly represented in the training data. In contrast, IRL provides learned reward function that offers valuable insights into the maaiing process, enhancing interpretability. Additionally, IRL enables the integration of explicit constraints directly into the reward function. can also model interactions between multi- ple agents by incorporating them into the inferred rewards, making it promising tool for improving the safety and so- cial acceptability for joint multi-agent trajectory prediction tasks. Moreover, by optimizing actions over the inferred reward function, IRL accounts for long-tern term consequences, allowing the agent to plan trajectories that are optimal over extended horizons. This not only enhances safety and effi- ciency but also facilitates seamless integration with down- stream Decision-making and motion planning modules.
In summary, while BC is effective in scenarios with well- represented data, IRL's ability to infer intentions, handle distribution shifts, and provide interpretability makes it a promising alternative for complex trajectory prediction tasks autonomous driving.
15


Reviews:
[{"review_id": "Xobmgxf9lg", "reviewer": "Reviewer_LLrG", "summary": "This paper presents Graph-oriented Inverse Reinforcement Learning (GoIRL), a novel IRL-based prediction framework that leverages vectorized context representations. The framework first extracts features from the vectorized inputs and then transforms them into grid space using a feature adaptor to ensure compatibility with existing IRL methods. To improve efficiency and accuracy, GoIRL employs a hierarchical, parameterized trajectory generator augmented with a refinement module that enhances both prediction accuracy and confidence. Extensive experiments demonstrate the effectiveness of the proposed design.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "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.\n\n1. **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.\n\n2. **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:\n|Method|brier-minFDE$_{6}$|Brier score|minFDE$_{6}$|minADE$_{6}$|MR$_{6}$|\n|:-|:-:|:-:|:-:|:-:|:-:|\n|HiVT|1.842|0.673|1.169|0.774|0.127|\n|GANet|1.790|0.629|1.161|0.806|0.118|\n|THOMAS|1.974|0.535|1.439|0.942|0.104|\n|GOHOME|1.983|0.533|1.450|0.943| 0.105|\n|HOME+GOHOME|1.860|0.568|1.292| 0.890|0.085|\n|GoIRL (Ours)|1.796|0.623|1.173|0.809|0.120|\n|GoIRL-Ens (Ours)|1.695|0.569|1.126|0.783|0.110|\n\n3. **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.\n\n**References**\n\n[1] HiVT: Hierarchical Vector Transformer for Multi-Agent Motion Prediction.\n \n[2] GANet: Goal Area Network for Motion Forecasting.\n\n[3] THOMAS: Trajectory Heatmap Output with Learned Multi-Agent Sampling. \n\n[4] HOME: Heatmap Output for Future Motion Estimation.\n\n[5] GOHOME: Graph-Oriented Heatmap Output for Future Motion Estimation.", "claims_and_evidence": "The claims are substantiated by thorough methodological descriptions and comprehensive experimental results.", "methods_and_evaluation_criteria": "Most recent motion forecasting methods adopt behavior cloning paradigms, which struggle with generalization and domain adaptation. These limitations become especially critical when the environment deviates significantly from the training distribution. In contrast, reinforcement learning (RL) offers a principled solution through its reward-driven learning and interaction-based training, rather than merely fitting to data distributions. Moreover, RL is also well-suited to address the modality collapse issues commonly observed in supervised learning approaches.", "theoretical_claims": "I have reviewed the IRL algorithms presented in the submission and did not identify any issues.", "experimental_designs_or_analyses": "This submission adopts standard evaluation metrics (ADE, FDE, MR) and widely-used datasets (Argoverse 1 and nuScenes) for experimental validation, which is fair and reasonable. However, given the availability of more challenging and diverse datasets such as Argoverse 2 and Waymo, the authors are encouraged to evaluate the proposed method on these benchmarks further to demonstrate its generalization capabilities better.", "relation_to_broader_scientific_literature": "This paper contributes to the broader scientific literature on motion forecasting by advancing the integration of inverse reinforcement learning (IRL) with vectorized map representations. Traditional approaches in motion forecasting predominantly follow behavior cloning (BC) paradigms, which are known to suffer from issues such as covariate shift and poor generalization to out-of-distribution scenarios. This work addresses these limitations by leveraging the reward-driven and interaction-based nature of IRL, positioning it as a more robust alternative to BC methods.", "essential_references_not_discussed": "To the best of the reviewer's knowledge, there is no existing work that closely resembles this research.", "other_strengths_and_weaknesses": "This submission is well-motivated, particularly in addressing the issue of covariate shift. It also provides a well-structured discussion of related work, clearly distinguishing between behavior cloning (BC) and inverse reinforcement learning (IRL) approaches. The proposed method is novel in several aspects: it effectively leverages rich information from vectorized representations and introduces a feature adaptor that enables compatibility with IRL methods. Furthermore, the hierarchical parameterized trajectory generator is designed to mitigate the inefficiencies commonly found in grid-based approaches.", "other_comments_or_suggestions": "N.A", "questions_for_authors": "The main concern is the omission of several commonly used baselines, such as:\n\n1. HiVT: Hierarchical Vector Transformer for Multi-Agent Motion Prediction\n2. GAMoNet: Goal Area Network for Motion Forecasting\n\nAlthough some of these methods may not be directly comparable—for instance, due to the use of more powerful scene encoders—they should still be included for completeness and to provide a broader context for comparison.\n\nMoreover, given that the proposed method operates in the grid representation space, it would be beneficial to include comparisons with other supervised grid-based approaches to better highlight its advantages:\n\n1. THOMAS: Trajectory Heatmap Output with Learned Multi-Agent Sampling\n2. GOHOME: Graph-Oriented Heatmap Output for Future Motion Estimation\n\nLastly, the paper would benefit from including more examples or case studies illustrating covariate shift, to further emphasize the importance and relevance of addressing this issue.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "RuS26pmMFa", "reviewer": "Reviewer_igcX", "summary": "The Graph-oriented Inverse Reinforcement Learning (GoIRL) framework is an IRL-based predictor that utilizes vectorized context representations. The author states that the proposed methods overcome the drawbacks of supervised learning techniques. Additionally, a hierarchical parameterized trajectory generator has been incorporated to enhance prediction accuracy. The experiments were conducted on two real-world datasets: Argoverse and nuScenes.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "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.\n\n1. **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.\n\n2. **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.\n\n3. **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:\n|Dataset|minFDE$_{1}$|minADE$_{1}$|MR$_{1}$|\n|:-|:-:|:-:|:-:|\n|Argoverse|3.365|1.551|0.539|\n|nuScenes|6.530|3.185|0.822|\n\n4. **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.\n\n5. **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.\n\n6. **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.\n\n7. **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.\n\n**References**\n\n[1] SingularTrajectory: Universal Trajectory Predictor Using Diffusion Model.\n\n[2] A Set of Control Points Conditioned Pedestrian Trajectory Prediction.\n\n[3] Trajectory Forecasts in Unknown Environments Conditioned on Grid-based Plans.\n\n[4] Travel Time-dependent Maximum Entropy Inverse Reinforcement Learning for Seabird Trajectory Prediction.\n\n[5] Can AI Predict Animal Movements? Filling Gaps in Animal Trajectories using Inverse Reinforcement Learning.", "claims_and_evidence": "Some claims made in the submission are problematic please refer to the weakness section.", "methods_and_evaluation_criteria": "The method evaluation makes sense for the problem of trajectory prediction.", "theoretical_claims": "Nil", "experimental_designs_or_analyses": "The soundness of the experimental designs looks correct.", "relation_to_broader_scientific_literature": "The paper contributes to a real-world application and plays an important role in autonomous driving, intelligent systems, navigation robots, and video surveillance.", "essential_references_not_discussed": "Nil", "other_strengths_and_weaknesses": "Strengths\n1.\tThe paper is well-written and easy to follow.\n The experimentation is thorough,\n2.\tThe results on two real-world datasets are promising, outperforming the compared methods.\n\n\nWeakness\n\nThe following are the weaknesses that need to be addressed to improve the manuscript:\n\nMotivation and Claims: \n\n1.\tIn Figure 1, the authors claim that “During the data collection process, the ground-truth trajectory is labeled as going straight.” However, no evidence is provided to support this claim. The authors should offer clarification or cite a source to validate this statement.\n\n2.\tFurthermore, the authors assert that existing supervised models can hardly react to such changes, which is not entirely accurate [1]. There are existing methods that incorporate collision avoidance behavior. For example, if there is a vehicle in front of the ego-vehicle, many models are designed to predict that the ego-vehicle will follow collision avoidance protocols and choose a safer maneuver, especially if such scenarios are present in the training data.\n\n[1] Meng, Dejian, et al. \"Vehicle trajectory prediction based predictive collision risk assessment for autonomous driving in highway scenarios.\" arXiv preprint arXiv:2304.05610 (2023).\n\n3.\tIn line 071, the author states, “Another critical concern associated with the supervised approach is the modality collapse issue.” This arises because the predictor must generate diverse and plausible predictions, yet many supervised methods tend to produce a single trajectory (deterministic prediction) [2]. Additionally, in exp., the author mentions K plans of 6 and 10; however, K = 1 is not included.\n\n[2] Bae, Inhwan, Young-Jae Park, and Hae-Gon Jeon. \"Singulartrajectory: Universal trajectory predictor using diffusion model.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.\n\n4.\tIs “recurrently forecasts control points to represent the trajectory” inspired by Graph-TERN [3]?\n\n[3] Bae, Inhwan, and Hae-Gon Jeon. \"A set of control points conditioned pedestrian trajectory prediction.\" Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 37. No. 5. 2023.\n\n\n\nNovelty\nThe main novelty of the paper lies in the use of MaxEnt IRL (Maximum Entropy Inverse Reinforcement Learning) for the multimodal trajectory prediction task. Existing literature [4,5] already addresses MaxEnt IRL in the context of trajectory prediction. The author should clearly distinguish between these methods as well. \n\n[3] Deo, Nachiket, and Mohan M. Trivedi. \"Trajectory forecasts in unknown environments conditioned on grid-based plans.\" arXiv preprint arXiv:2001.00735 (2020).\n[4] T. Hirakawa, T. Yamashita, K. Yoda, T. Tamaki, and H. Fujiyoshi, \"Travel Time-dependent Maximum Entropy Inverse Reinforcement Learning for Seabird Trajectory Prediction,\" in Asian Conference on Computer Vision, pp. 430-435, 2017.\n[5]\tT. Hirakawa, T. Yamashita, T. Tamaki, H. Fujiyoshi, Y. Umezu, I. Takeuchi, S. Matsumoto, K. Yoda, \"Can AI predict animal movements? Filling gaps in animal trajectories using Inverse Reinforcement Learning,\" Ecoshere, vol 9, no. 10, pp. e02447, 2018.\n\n\nExperimentation\n\n1.\tIn Table 4, the addition of the Bezier curve results in only a minor improvement. The authors should explain why the Bezier curve contributes so little to the overall performance.\n2.\tAdditionally, what is the baseline implementation, and which result in Table 4 corresponds to the baseline? This should be clearly stated to help readers understand the comparative performance of the proposed method.", "other_comments_or_suggestions": "Nil", "questions_for_authors": "Please see Weaknesses", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "jiUVjMgh0i", "reviewer": "Reviewer_PdeW", "summary": "GoIRL is a graph-based inverse reinforcement learning framework for predicting multiple possible future trajectories in autonomous driving. It integrates lane-graph features into IRL, uses a hierarchical decoder for accurate predictions, and outperforms supervised models on Argoverse and nuScenes benchmarks.\n\n## Update after rebuttal\n\nIn the rebuttal, the authors included the model’s performance on the AV2 leaderboard, enhancing the comprehensiveness of the evaluation. They also presented quantitative results on Drivable Area Changes, which help illustrate the method’s potential for generalization in such scenarios.\n\nHowever, the performance of GoIRL still lags significantly behind the state-of-the-art method LOF (B FDE 1.63 vs. 1.76). Furthermore, the specific advantage offered by IRL in generalizing to drivable area changes remains unclear. The necessity of addressing this problem through IRL is questionable—alternative approaches, such as prediction models conditioned on the road graph, can also adhere strictly to the drivable area.\n\nOverall, given that the absolute performance is not improved and that the claim of generalizability to drivable area changes seems somewhat ill-posed, I assign a weak reject as my final rating. I recommend conducting additional experiments and comparisons focused on more challenging long-tail generalization scenarios (e.g., drivable area changes, sudden pedestrian emergence) to more convincingly demonstrate the benefits of using IRL. A comparison with SOTA models on such challenging setting would significantly strengthen the paper.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "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.\n\n### **1. Choice of Benchmark Datasets & Recent Baselines.**\nWe acknowledge the reviewer’s concerns regarding dataset and baseline selection and provide our response as follows:\n\n(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:\n  - Our supervised graph-based baseline (DSP [1]) was originally evaluated on Argoverse, ensuring a fair and rigorous comparison with our proposed IRL framework. \n  - 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. \n  - 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.\n\n(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.\n|Method|brier-minFDE$_{6}$|Brier score|\n|:-|:-:|:-:|\n|LOF|1.658|0.626|\n|QCNet|1.693|0.626|\n|GoIRL (Ours)|1.695|0.569|\n\n(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.\n\n### **2. Evaluation for Generalization in Drivable Area Changes.**\nWe 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.\n|Method|Success Rate|\n|:-|:-:|\n|DSP|15.87%|\n|GoIRL (Ours)|88.13%|\n\n**References**\n\n[1] Trajectory Prediction with Graph-based Dual-Scale Context Fusion.\n\n[2] Trajectory Forecasts in Unknown Environments Conditioned on Grid-based Plans.\n\n[3] FutureNet-LOF: Joint Trajectory Prediction and Lane Occupancy Field Prediction with Future Context Encoding.\n\n[4] Query-Centric Trajectory Prediction.", "claims_and_evidence": "1. GoIRL is the first to integrate the MaxEnt IRL paradigm with vectorized context representation.\nThis claim appears to be true and highlights the novelty of the proposed approach.\n2. GoIRL proposes a hierarchical parameterized trajectory generator and an MCMC-augmented probability fusion method for improved performance.\nThis claim is well-supported by the ablation study, which clearly demonstrates the performance benefits of each component.\n3. It achieves state-of-the-art performance on two large-scale motion forecasting benchmarks.\nThis claim is well-supported by the quantitative results presented in the paper.\n4. It demonstrates superior generalization abilities compared to existing supervised models in handling drivable area changes.\nThis claim lacks sufficient evidence. The paper provides only a single qualitative example, which is not enough to conclusively support the generalization claim.", "methods_and_evaluation_criteria": "The proposed method leverages Inverse Reinforcement Learning (IRL) to address compounding error and generalizability issues, which is a reasonable and well-motivated approach. Prior work has demonstrated the effectiveness of IRL in similar contexts.\n\nHowever, the benchmark datasets used in the paper are outdated. Argoverse (2019) and nuScenes (2020) are no longer actively maintained or considered state-of-the-art. More recent and widely adopted benchmarks, such as Argoverse 2 and the Waymo Open Motion Dataset, are not used. As a result, the validity of the claimed improvements is questionable, especially since strong baselines on these newer benchmarks (e.g., MTR, QCNet, LOF) are not included in the comparisons.\n\nAdditionally, the evaluation metrics are not comprehensive. The paper claims superior generalization ability, yet provides no quantitative experiments to support this assertion.", "theoretical_claims": "The theoretical claims look good to me in this paper.", "experimental_designs_or_analyses": "Please see the 'Methods And Evaluation Criteria*' part", "relation_to_broader_scientific_literature": "This paper leverages previous findings in Inverse Reinforcement Learning.", "essential_references_not_discussed": "none", "other_strengths_and_weaknesses": "Please see above", "other_comments_or_suggestions": "none", "questions_for_authors": "none", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Ah8Lkl82U0", "reviewer": "Reviewer_ZXUe", "summary": "This paper focuses on the problem of trajectory prediction, which is hard because of the inherent uncertainty and underlying multimodality. Previous method mainly focuses on behavior cloning, which has been shown to have a covariant shift problem. Therefore, this paper proposes to use IRL to solve this problem. In particular, the authors propose a Graph-oriented Inverse Reinforcement Learning (GoIRL) framework, which is an IRL-based predictor equipped with vectorized context representations. They develop a feature adaptor to effectively aggregate lane-graph features into grid space, enabling seamless integration with the maximum entropy IRL paradigm to infer the reward distribution and obtain the policy. Extensive experimental results show that the proposed approach not only achieves state-of-the-art performance on the large-scale Argoverse & nuScenes motion forecasting benchmarks but also exhibits superior generalization abilities compared to existing supervised models.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "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.\n\n1. **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.\n|Method|brier-minFDE$_{6}$|Brier score|minFDE$_{6}$|minADE$_{6}$|MR$_{6}$|\n|:-|:-:|:-:|:-:|:-:|:-:|\n|AutoBot|2.057|0.685|1.372| 0.876|0.164|\n|GoIRL (Ours)|1.796|0.623|1.173|0.809|0.120|\n\n2. **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.\n\n3. **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.\n\n4. **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. \n\n5. **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.\n\n6. **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.\n\n**References**\n\n[1] Trajectory Prediction with Graph-based Dual-Scale Context Fusion.\n\n[2] Trajectory Forecasts in Unknown Environments Conditioned on Grid-based Plans.\n\n[3] Latent Variable Sequential Set Transformers for Joint Multi-Agent Motion Prediction.\n\n[4] https://en.wikipedia.org/wiki/Domain_adaptation.", "claims_and_evidence": "Yes.", "methods_and_evaluation_criteria": "Yes.", "theoretical_claims": "No theoretical claims.", "experimental_designs_or_analyses": "Yes.", "relation_to_broader_scientific_literature": "Trajectory prediction is an important task in autonomous driving.", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "Strengths:\n\n1.\tIn general, this paper is well-written and easy to follow. The figures are clear and illustrative to understand.\n2.\tThe idea of using IRL to solve the trajectory prediction task is interesting and promising, it has the potential to avoid covariant shift problems in behavior cloning.\n\nWeaknesses:\n\n1.\tSome recent trajectory prediction methods are missing. Although this paper focuses on graph-based representation and IRL, it focuses on a well-studied area that has rapid development and new algorithms. I think one reason is that the most recent work focuses on the waymo dataset, which is larger than argoverse and nuScenes. I think the authors should also include results on the Waymo dataset and compare the SOTA methods in the leaderboard. In particular, I think autoregressive models with tokenized representation have recently become popular and promising and should be considered as baselines.\n2.\tNot enough qualitative examples are shown in the paper. Figures 4, 5, and 7 only show the multi-modal prediction of a single vehicle scenario. I think the biggest problem in trajectory prediction is learning the interaction between diverse agents. The authors may need to show more examples of the interactive scenarios with multiple agents, together with the comparison with baseline models.\n3.\tLoss function (12) might be too complex to tune for different datasets.", "other_comments_or_suggestions": "No.", "questions_for_authors": "1.\tThe covariate shift example in Figure 1 is confusing. If the barricade is included in the observation and there are training samples that contain similar situations, I think the predictor will only predict a left turn. If there is no barricade seen in the training sample, then the model fails because of the out-of-distribution problem rather than the covariant shift.\n2.\t“We employ the target-centric coordinate system, where all context instances and sequences are normalized to the current state of the target agent through translation and rotation operations.” The efficiency of using “target-centric” representation could be low when we need to predict the trajectory of all agents. Can this proposed method be integrated into query-centric representation?\n3.\tOn page 7 line 375, the authors say “Furthermore, we adopt an ensemble strategy (Zhang et al., 2024) to boost prediction performance”. How does this ensemble work? Do methods in Table 3 also use ensemble?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "P4BoK46uUT", "reviewer": "Reviewer_DqsN", "summary": "In this paper, the authors introduce a Graph-oriented Inverse Reinforcement Learning (GoIRL) framework for multimodal trajectory prediction. Specifically, (1) to capture the complex scene context in a structured manner, they use vectorized representations of the environment (scene features), (2) to integrate detailed lane information into the prediction model, they aggregate lane-graph features into a grid space, allowing the model to understand the spatial relationship and constraints of the driving environment, (3) they utilizes a hierarchical parameterized trajectory generator for improving prediction accuracy and an Markov chain Monte carlo (MCMC)-augmented probability fusion for boosting prediction confidence.\n\n## update after rebuttal\nI gave a 'weak accept\" score because Combining the IRL and graph-based context encoding is a good try in trajectory prediction. Thanks.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "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.\n\n1. **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.\n\n2. **Recent Solutions & References.** We greatly appreciate the reviewer’s recommendations for recent solutions. The referenced works propose different paradigms:\n   - Ref. [1] employs a self-supervised approach leveraging all data (including the test set) for pertaining.\n   - Ref. [2] introduces a powerful query-centric paradigm for scene encoding within a supervised learning paradigm.\n   - Ref. [3] focuses on improving out-of-distribution generalization by introducing a novel evaluation protocol.\n\n    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.\n\n3. **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.\n\n4. **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.\n\n5. **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.\n   - Figure 1(a) illustrates how poor observations of static or slow-moving agents can negatively impact trajectory predictions.\n   - Figure 1(b) demonstrates that inaccuracies in speed prediction can affect longitudinal accuracy.\n   - Figure 1(c) highlights a limitation where the model fails to predict a lane change in the absence of explicit cues.\n\n    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.\n\n6. **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.\n\n7. **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.\n\n**References**\n\n[1] SEPT: Towards Efficient Scene Representation Learning for Motion Prediction.\n\n[2] QCNeXt: A Next-Generation Framework for Joint Multi-Agent Trajectory Prediction.\n\n[3] Improving Out-of-Distribution Generalization of Trajectory Prediction for Autonomous Driving via Polynomial Representations.", "claims_and_evidence": "Overall, claims made in this paper are supported by evidence. \n1. The GoIRL framework integrates MaxEnt IRL with vectorized context representations has corresponding detailed explanation. The Section 3 provides detailed descriptions of the framework and related operations. \n2. The claim about the performance “achieves state-of-the-art performance on the large-scale Argoverse & nuScenes” is supported by the quantitative results reported in Table 1, 2, and 3. In these tables, the authors compare their solutions with other existing solutions. \n\nThere are several recent works shown in the Argoverse motion forecasting page https://paperswithcode.com/sota/motion-forecasting-on-argoverse-cvpr-2020. \nIt will be better to compare the proposed solution with some existing solutions rank top on this page.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria make sense for the trajectory prediction task. It will be better, if the authors could report the accuracy for each prediction step. In this case, readers may get more sense about the performance of the proposed solution, e.g., the model performs better at the first few steps and the performs worse at the last step, etc.", "theoretical_claims": "This paper does not have challenging mathematical proofs or theoretical claims. The model operations and loss functions used in this paper look reasonable and should work for the trajectory prediction task.", "experimental_designs_or_analyses": "Overall, the experimental designs and analyses make sense. However, as mentioned above, it will be better to compare the proposed solution with more existing solutions to prove the effective of the proposed solution.", "relation_to_broader_scientific_literature": "The proposed solution combines the Inverse Reinforcement Learning with graph-based context to improve prediction performance and generalization. To achieve this goal, there are several components of this paper were adapted from existing work. For example:\n1. Context Encoder:  the Dilated LaneConv operator proposed in LaneGCN is applied. \n2. Policy Generator: followed the MaxEnt IRL framework.", "essential_references_not_discussed": "It will be better if the authors could discuss more recent work, for example:\n\n* Lan, Zhiqian, Yuxuan Jiang, Yao Mu, Chen Chen, and Shengbo Eben Li. \"Sept: Towards efficient scene representation learning for motion prediction.\" arXiv preprint arXiv:2309.15289 (2023).\n* Zhou, Zikang, Zihao Wen, Jianping Wang, Yung-Hui Li, and Yu-Kai Huang. \"Qcnext: A next-generation framework for joint multi-agent trajectory prediction.\" arXiv preprint arXiv:2306.10508 (2023).\n* Yao, Yue, Shengchao Yan, Daniel Goehring, Wolfram Burgard, and Joerg Reichardt. \"Improving Out-of-Distribution Generalization of Trajectory Prediction for Autonomous Driving via Polynomial Representations.\" In 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 488-495. IEEE, 2024.", "other_strengths_and_weaknesses": "Other Strengths:\n1. Combining the IRL and graph-based context encoding is a good try in trajectory prediction. The purpose of the usage of the inference learning is explained clearly and makes sense. \n2. The framework design should be generalize well to new data and different domains. \n\nOther Weaknesses:\n1. It will be better to report the complexity of the proposed solution. The integration of multiple components make the framework complex, and may involve challenges in real world use case. Reporting the complexity/latency of the solution will be helpful to readers. \n2. The performance of the model may rely on the quality of training data. For example, the accuracy of the lane-graph feature, observed trajectories, etc. It will be better to report the performance with noisy inputs.", "other_comments_or_suggestions": "1. It will be better to report some failure cases, and make some discussions about the failures.\n2. The interpretability of the proposed model is also a concern. It will be better to come up with a way to improve the interpretability of model’s predictions.", "questions_for_authors": "1. Do we need to use different grid space for different scenes/datasets?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: The paper got mixed review. After carefully reading all reviews, the AC believes that the combination of IRL with graph-based representations and grid space is both novel and effective. We agree with reviewers "DqsN" and "LLrG": 
"This paper contributes to the broader scientific literature on motion forecasting by advancing the integration of inverse reinforcement learning (IRL) with vectorized map representations". Using a feature adaptor to bridge vectorized maps with grid-based IRL is a an idea worth publishing that helps retain important scene information while enabling efficient prediction. The MaxEnt IRL approach does a good job capturing uncertainty, and the hierarchical decoder with Bézier curves adds smoothness and accuracy to the predicted trajectories.

The results on Argoverse and nuScenes are strong, outperforming several supervised baselines. The generalization to unseen scenarios, like changes in drivable areas, is impressive. Yet, we also agree on the weaknesses raised by other reviewers on the performance on other datasets. We invite the authors to address them for their camera-ready e.g., "While GoIRL may slightly underperform recent strong baselines such as LOF on certain metrics like brier-minFDE, we believe further gains could be realized through targeted hyperparameter fine-tuning."
Decision: Accept (poster)