CausalAF: Causal Autoregressive Flow for Safety-Critical Driving Scenario Generation
Authors: Wenhao Ding
Haohong Lin
Bo Li
Ding Zhao
Venue: CoRL 2022 Poster (2022)
Keywords: Causal Generative Models
Scenario Generation
Autonomous Driving

Abstract: Generating safety-critical scenarios, which are crucial yet difficult to collect, provides an effective way to evaluate the robustness of autonomous driving systems. However, the diversity of scenarios and efficiency of generation methods are heavily restricted by the rareness and structure of safety-critical scenarios. Therefore, existing generative models that only estimate distributions from observational data are not satisfying to solve this problem. In this paper, we integrate causality as a prior into the scenario generation and propose a flow-based generative framework, Causal Autoregressive Flow (CausalAF). CausalAF encourages the generative model to uncover and follow the causal relationship among generated objects via novel causal masking operations instead of searching the sample only from observational data. By learning the cause-and-effect mechanism of how the generated scenario causes risk situations rather than just learning correlations from data, CausalAF significantly improves learning efficiency. Extensive experiments on three heterogeneous traffic scenarios illustrate that CausalAF requires much fewer optimization resources to effectively generate safety-critical scenarios. We also show that using generated scenarios as additional training samples empirically improves the robustness of autonomous driving algorithms.

CausalAF: Causal Autoregressive Flow for Safety-Critical Driving Scenario Generation
Wenhao Ding', Haohong Lin', Bo Li,, Ding Zhao'
Carnegie Mellon University
University of Illinois at Urbana-Champage
(wenhaod, haohong fandrew.cmu cmu edu, 1bo0i mooiillinois weooissecce edu, dingzhac@cmu, .dd
Abstract: Generating safety-critical scenarios, which are crucial yet difficult to collect, provides an effective way to evaluate the robustness of autonomous driving systems. However, the diversity of scenarios and efficiency of generation methods are heavily restricted by the rareness and structure of safety-critical scenarios. Therefore, existing generative models that only estimate distributions from obser- vational data are not satisfying to solve this problem. In this paper, we integrate causality as a prior into the scenario generation and propose a flow-based generative framework, Causal Autoregressive Flow (CausalAF). CausalAF encourages the generative model uncover and follow the causal relationship among generated objects via novel causal masking operations instead of searching the sample only from observational data. By learning the cause-and-effect mechanism of how the generated scenario causes risk situations rather than just learning correlations from data, CausalAF significantly improves learning efficiency. Extensive experiments on three heterogeneous traffic scenarios illustrate that CausalA F requires much fewer optimization resources to effectively generate safety-critical scenarios. We also show that using generated scenarios as additional training samples empirically improves the robustness of autonomous driving algorithms.
Keywords: Causal Generative Models, Scenario Generation, Autonomous Driving
Introduction
According recent report [l], several companies have made their autonomous vehicles (AVs) drive more than 10,000 miles without disengagement. It seems that current AVs have achieved great success in normal scenarios that cover most cases in daily life. However, we are still unsure about their performance under critical cases, which could be too rare to collect in the real world. For example, kid suddenly running into the drive lane chasing a ball leaves the AV a very short time to react. This kind of situation, named safety-critical scenarios, could be the last puzzle to evaluate the safety of AVs before deployment.
Generating safety-critical scenarios with Deep Generative Models (DGMs), which estimate the distribution of data samples with neural networks, is viewed as promising way in recent works [2]. Existing literature either searches the latent space to build scenarios [3, 4] or directly uses opti- mization find the adversarial examples [5, 6]. However, such a generation task is still challenging since we are required simultaneously consider fidelity to avoid conjectural scenarios that will never happen in the real world, well the safety-critical level which is indeed rare compared with normal scenarios. In addition, generating reasonable threats to vehicles' safety be inefficient if the model purely relies on unstructured observational data, as the safety-critical scenarios are rare and follow fundamental physical principles. Inspired by the fact that humans are good at abstracting the causation beneath the observations with prior knowledge, we explore a new direction toward causal generative models for this generation task.
6th Conference Robot Learning (CoRL. 2022), Auckland, New Zealand.

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To have a glance at causality in traffic scenarios, we show an example in Figure 1(b). When vehicle B is parked in the middle between the autonomous vehicle and pedestrian C, the view of A is blocked. making A have little time to brake and thus have potential collision with C. As human drivers, we believe B should be the cause of the accident. This scenario may take AVs millions of hours to collect [7]. Even we use traditional generative models to gen- erate this scenario, rize the location of all objects without learning the reasons. As remedy, we can incorporate causality into generative models for the efficient generation of such safety-critical scenarios.
(a)
CausalAF
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Exerutor
COM
CVM
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Simulator
Tested Venicle
Graph
Behavioral Graphs
(b)
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A
B
A
B
M
time
In this paper, we propose structured generative model with causal priors. We model the causal- ity as directed acyclic graph (DAG) named Causal Graph (CG) [8]. To facilitate CG in the traffic scenario, we propose another Behavioral Graph (BG) for representing the interaction be- tween objects in scenarios. The graphical repre- sentation of both graphs makes possible to use the BG to unearth the causality given by CG. Based on BG, we propose the first generative model that integrates causality into the graph generation task and names it CausalAF. Specifically, we propose two types of causal masks Causal Order Masks (COM) that modifies the node order for node generation, and Causal Visibility masks (CVM) that removes irrelevant information for edge generation. We show the diagram of CausalAF generation in Figure (a) and summarize our main contributions as following:
brake
brake
Figure I: (a) Diagram of the generation pipeline using CausalAF. (b) Two scenarios obtained by two Behavioral Graphs shows the causality behind scenarios. The top one is safety-critical because view vehicle A is blocked by vehicle B.
We propose a causal generative model CausalAF that integrates causal graphs with two novel mask operators for safety-critical scenario generation.
We show that CausalAF dramatically improves the efficiency and performance on three standard traffic settings compared with purely data-driven basclines.
We show that the training on generated safety-critical scenarios improves the robustness of reinforcement learning- boaning-based driving algorithms.
2
Graphical Representation of Scenarios
We start by proposing novel representation of traffic scenarios using a graph structure. Then, we propose to generate such a graphical representation with an autoregressive generative model.
2.1 Behavioral Graph
Traffic scenarios mainly consist of interactions between static and dynamic objects, which can be naturally described by graph structure. Therefore, define Behavioral Graph g to represent driving scenarios with the following definition.
Definition 1 (Behavioral Graph, BG). Suppose scenario has maximum objects with types. A Behavioral Graph G = (VB EB) is a directed graph with node matrix V pg representing the types of objects and edge matrix E mmmxm (kg+tgg representing the interaction between objects, where h1 is the number of edge types and h2 is the dimension of edge altributes.
According to this definition, GB works as a planner that controls the behaviors of objects in the scenario based on the types of nodes B and edges E For example, nodes i and U2 represent two vehicles and the edge from to U2 represents the relative velocity from U1 to V2. Specifically, self-loop edge (i, i) represents that one object takes one action irrelevant to other objects (e.g.,

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car goes straight or turns left with no impact on other road users), while other edges (i.j) means object i takes one action related to object j (e.g., a car i moves towards a pedestrian j). The edge attributes represent the properties of actions. For instance, the attribute [ær, y, Uzz Uyl of one edge has the following meaning: z: and y are positions, and U, and By are the velocities.
2.2 Behavioral Graph Generation with Autoregressive Flow
Generally, there are two ways to generate graphs: one is simultaneously generating all nodes and edges, and the other is iteratively generating nodes and adding edges between nodes. Considering the directed nature of g we utilize the Autoregressive Flow model (AF) [9], which is a type of sequentially DGMs, to generate nodes and edges of G step by step. It uses a invertible and differentiable transformation Fe parametrized by & to convert the graph G a latent variable that follows a base distribution p(=) (e.g.. Normal distribution A/O0, I)). According to the change of variables theorem, we obtain (G (FFF((B)) det
0F,19 .o increase the representing ag
capability, Fø contains multiple functions f. for {o..... K]. The entire transformation is represented as G zk JK ..... fo غ F (zo) by repeatedly substituting the variable for the new variable 2,, where o means the function composition. Eventually, we obtain the likelihood
K
log log = p(zo)
Σ
log det
dz,-1
which will be used learn the parameter & based on empirical distribution of g After training. can sample from pa (GB) by using the reverse function Fz² Let Vi R and [[. Rhitha
represent node and edge (1.5) of G then we can generate them with the sampling procedure:
B ~ N' (n) (o,)) μ. + +o O and [. N (Kyy (og)) = pij + oo Oc, [
(2)
where @ denotes the element-wise product and follows Normal distribution (0, I). Variables Mr of Mij. and ofj are obtained from Fo in an autoregressive manner:
p = Fo ( (1) L fo: 1,0m)) and Pij. oi = Fo (v
(0:i) L (0..000-11)
(3)
where [0: i] represents the elements from index 0 to index After the sampling, we obtain the node and edge type by converting V and part of En from continuous values one-hot vectors:
Vi f- onehot arg maxmmaa))) (V ).
EB [....u:,)) f- onehot arg max E (B/),,....)) Vi,j E [m].
(4)
Intuitively, the generation of one node depends all previously generated nodes and edges. One node only has edges pointing to the nodes that are generated before it. To illustrate this autoregressive generation process, we provide an example with three nodes in Figure 2(a).
3 Causal Autoregressive Flow (CausalAF)
In this section, we discuss how to integrate causality into the autoregressive generating process of the Behavioral Graph gB In general, we transfer the prior knowledge from causal graph to g by increasing the structural similarity. However, calculating such similarity is not easy because of the discrete nature of graphs. To solve this problem, propose CausalAF with two causal masks, i... Causal Order Masks (COM) and Causal Visible Masks (CVM), that make the generated G follow the causal information.
3.1 Causal Generative Models
Definition (Structural Causal Models [10], SCM). structural causal model (SCM) = (S,U) consists of collection of m functions, Xj = fP Ug), Vj [m], where PA, C {X1,..., XxX)(Xx)) are called parents of Xz: and joint distribution U (UI,..., Um over
the noise variables, which are required to be jointly independent.
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COM 7
Ar and 3g21
CVM Ain
CVM
Queue Q
Ar and
i-0
COM
1-2
Causel Graph
Behavioral Graph
CVM
N
CVM
Queue
b-+b
(c)
Bb
COM
i-2
bbb
Queue Q
-OWE Apply CVM
Apply
Generstion Erge
Figure 2: (a) The generation process of BG, which starts from empty graph. We add one node or one edge at each step. COM is applied to select nodes following the CG and CVM is applied to mask out non-parem nodes following the CG. (b) CG and BG used in the example. (c) The explanation of CVM when generating edges for c, where irrelevant node ó is masked out in both V and E
Definition 3 (Causal Graphs [10], CG), The causal graph G of an SCM is obtained by creating one node for each Xj and drawing directed edges from each parent in PAj(G() to Xj. The representation of G = SyC,E"" consists of the node vector VC E {0, 13 and the adjacency matrix F. E {0, 1] 1]mxxxxs, Each edge (i,j) represents a causal relation from node i to node j.
We formally describe the causality based on the above definitions of SCM and CG. In fact, the generative model (P mentioned in Section shares very similar definition with SCM except that G does not follow the order of causality. This inspires us that we can convert (G to an SCM by incorporating the causal graph G into the generation process. In this paper, we assume the causal graph G can be summarized by expert knowledge. Therefore, we incorporate given Go into Ps (G (C)) by regularizing the generative process with two novel masks as shown in Figure 2.
3.2 Causal Graph Integration
Causal Order Masks (COM) The order is vital during the generation of G since we must ensure the cause is generated before the effect. To achieve this, we maintain priority queue Q to store the valid child types according to the causal relation in g Q is initialized with Q = { PG
0. Vi E [m]], which contains all nodes that do not have parent nodes. Then, in each node generation step, we update Q by removing the generated node and adding the child nodes of i. Since one node may have multiple parents thus is valid only all of its parents have been generated. We use Q to create a h-tot mask M0 E R", where the element is set to if it is valid type. Then, apply COM to the node matrix by VBB +- M @ Vi. where V is the node vector obtained from F for node i. Intuitively, this mask sets the probability of the invalid node types to 0 to make sure the generated node always follows the correct order.
Causal Visible Masks (CVM) Ensuring correct causal order still insufficient to represent the causality. Thus, we further propose another type of mask called CVM, which removes the non-causal connections, i.e., non-parent nodes to the current node in go, when generating edges. Specifically, we generate two binary masks 2 E Ruxn and M2,1 E R.m fmmxx((1)) (hx) with MM = 0 and M [. = 0 Vj & PAG(GC). Then, we apply them to update the node matrix and edge matrix by y + M B and E < 2 o E We illustrate an example of this process in Figure 2(c). Assume we are generating edges for node c. We need remove node since go tells us that B does not have edges node C. After applying M and M we move the features of node to the previous position of b. This permuting operation is important since the autoregressive model is not permutation invariant.

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3.3 Optimization of Safety-critical Generation
After introducing the generative process of CausalAF, we now turn to the optimization procedure. The target is to generate scenarios T = E( with am executor & to satisfy given goal, which is formulated as an objective function Lg. We define (r) ( < c), where ((T) represents the minimal distance between the autonomous vehicle and other objects and is small threshold. Therefore, the optimization is to solve the problem maxş "G ( (E(G))) Usually, Lg contains non-differentiable operators (c.g.. complicated simulation and rendering). thus we have to utilize black-bor box optimization methods to solve the problem. We consider a policy gradient algorithm named REINFORCE [11], which obtains the estimation of the gradient from samples by
V (0
E a log p(G ( (E((BB
(5)
Overall, the entire training algorithm is summarized Algorithm 1. In addition, we can prove that the CausalAF guarantees monotonicity of likelihood in Theorem 1 at convergence. The detail of the proof is given in Appendix A.
Theorem 1 (Monotonicity of Likelihood). Given the true causal graph g = -VC ECd and distance SHD [12], for CG of (VC, ET) and G (VC, (VC,E)) if SHD got) SHD g. and 3 e, s.t. E Ufc} ES, CausalAF converges with the monotonicity of likeli- hood for collision samples, iee. Po (D(T) < c <()gg) < (D(T( < c (99 < <D((TT)) < << <l)g").
3.4 Scenario Sampling and Execution
Training process of CausalAF Input: Causal Graph g Goal E.g. Learning rate a, Maximum node number m
Algorithm 1:
Thanks to the autoregressive generation of CausalAF, we are able to conduct generation conditioned on arbitrary numbers or types of nodes. Instead of generating from the seratch, we can start from an existing Ge for the genera- tion with GD ~ Po(-Ig," go) The conditional generation can be used for interactive scenarios, e.g. using the autonomous vehicle's informa- tion or the data of partial scenarios in the real world as conditions to generate diverse and re- alistic scenarios. After sampling the scenarios, the physical properties (e.g.. position and veloc- ity) defined in the generated G are executed in the simulator & to create sequential scenarios T. After the execution, the simulator outputs the objective function (T) as the result.
while & not converged do BG G Ps(99199)
// Sample for i < m do
Sample node matrix by (2)
[8]
Get node type V by (4)
Apply COM M to V
Apply CVM MI. M2 to V.B. EB
M (al
for j
S do
Sample edge matrix ERg by (2)
Get edge type E by (4)
[5.5]
Collect one scenario g = (V EB
// Learn model parameters Calculate the likelihood p (g Execute E() and get Eg (T) Use (5) to update + Φ a a (T)
Experiment
We evaluate CausalAF using three top pre-crash traffic scenarios defined by U.S. Department of Transportation [13] and Euro New Car Assessment Program [14]. Our empirical results show that may not be trivial for the generative models to learn the underlying causality even if such causality seems understandable to humans. Particularly, we conduct a series of experiments to answer the following main questions: Q1: How does CausalAF perform compared to other scenario generate methods? Q2: How does causality help the generation process? Q3: How can we use the generated safety-critical scenarios? In this section, we will first introduce the designed environment and baseline methods. Then we will answer the above questions by carefully investigating the experiment results.
4.1 Experiment Design and Setting
Scenario. We consider three safety- traffic scenarios (shown in Figure 3) that have clear causation. The causal graph g for each scenario is displayed on the upper right of the scenario.
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Pedestrain (P nods)
Traffic Light node)
Autonomous vehicle
node)
Inelevant vehicle
node)
AmM
Risk vehicle
Static vahicle node)
Collision
(C nooe)
(a) Intersection
(b) Crossing
(c) Highway
Figure Three causal traffic scenarios are used in our experiments. The corresponding causal graphs are shown in the upper right of each scenario. Please refer to Section 4.1 for details.
Table Collision rate (1) of generated safety-critical scenarios. Bold font means the best.
Method
[5]
[MG [15
STRIVE [16]
Baseline
Baseline+COM CausalAF
Intersection
0.63+0.28
0.31+0.54
0.47:0.61 0.6410.12
0.29:10.84
0.69:10.22
0.98=10001
Crossing
0.69=#0.41
0,43+00.56
0.38 0.55++0.10
0.355+00.5
0.57+0048
0.83--0.13
Highway
0.85+0010
0.56+-0.36
0.58 0.67+-0.16
0.53++0.69 0.88++0.44
0.91+-0.06
Intersection. One potential
critical event could happen when the traffic light T turns from green yellow to give the road right autonomous vehicle A. Here, A and R are influenced by T. R runs the red light, colliding with A perpendicularly, therefore, causing the collision C together with A. I does not influence other objects.
Crossing. A pedestrian P and autonomous vehicle A are crossing the road in vertical directions. There also exists static vehicle S parked by the side of the road. Then potentially risky scenario could happen when S blocks the vision of A. In this scenario, S is the parent of A, and P and A cause the collision C. I does not influence other objects.
Highway. An autonomous vehicle A takes lane-changing behavior due to a static car S parked in front of it. Meanwhile, a vehicle I drives in the opposite lane. Since S blocks the vision of A, is likely to collide with R. In this scenario, the parent of A, and and A cause the collision C. does not influence other objects.
Simulator.
We implement the above scenarios in 2D simulator, where all agents have radar sensors and are controlled by simple vehicle dynamic. During the running, the autonomous vehicle is controlled by rule-based policy, which will decelerate it detects any obstacles in front of it within a certain range Thus, the safety-critical scenario will not happen unless the radar of one agent is blocked and the distance is smaller than the braking distance, avoiding the creation unrealistic scenarios. The action space contains the acceleration and steering of all objects, and the state space contains the position and heading of all objects and the status of traffic lights if applicable.
Baselines. We consider 7 algorithms baselines, including 5 scenario generation methods and 2 variants of our CausalAF. Learning to collide (L2C) [5] uses a Bayesian network to describe the relationship between objects. Multi-modal Generation (MMG) [4] uses an adaptive sampler to increase sample diversity. STRIVE [16] learns traffic prior from datasets and uses adversarial optimization to generate risk scenarios. SAC is standard RI. algorithm using the objective as reward function. To further investigate the contribution of COM and CVM, we design two variants that share the same network structure CausalAF, Baseline does not use COM CVM, and Baseline+COM only uses COM.
4.2 Results Discussion
How does CausalAF perform on safety-critical scenario generation? (Q1) We train all generation methods in 3 environments and report the final objective values in Table We observe that CausalAF achieves the best performance among all methods. I.2C performs better than MMG and SAC because it also considers the structure of the scenario. We also notice that both Baseline and Baseline+COM have performance drops compared to CausalAF, indicating that the COM and CVM modules contribute to the autoregressive generating process. Baselinc+COM performs a little better

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(4) Tigh
(b) Padestrain
Lame-dhanging
2.00
8.50
0.50-
Orjectvv
6.25
0.5
0.25
6.32
8.00
0.00
Bale (Todk
Racii (Trdu))
Moseice -4.0
Coussior (hx4.1
0.50
Coureil TT-355
66.55
Texe
-8.75
our (he))
-0.15
:000 (h-0)
-3.98
-1.00
Counali (--31
-1.00
Cauorill (T-2)
300
200
Nooratoon
Ionation
Figure 4: Training objective Lg of CausalAF and two variants under two sampling temperatures.
The higher the sampling temperature is, the more diverse the generated scenarios are.
Table 2: Collision rate of RL algorithms evaluated in different scenarios.
Intersection
Crossing L2C MMG
Highway L2C
Method
Norm
L2C MMG Ours
Norm
Ours
Norm
MMG
Ours
SAC-Norm
0.05
0.57
0.64
0.91
0.04
0.54
0.67
0.92
0.03
0.79
0.75
0.95
SAC-Ours
0.01
0.03
0.04
0.08
0.00
0.04
0.06
0.11
0.02
0.01
0.04
0.09
PPO-Norm
0.07
0.44
0.48
0.86
0.03
0.53
0.61
0.80
0.02
0.62
0.64
0.92
PPO-Ours
0.00
0.04
0.01
0.12
0.02
0.03
0.03
0.08
0.01
0.02
0.03
0.13
DDPG-Norm
0.12
0.76
0.62
0.89
0.07
0.71
0.76
0.85
0.04
0.72
0.61
0.95
DDPG-Ours
0.01
0.02
0.05
0.13
0.02
0.01
0.04
0.12
0.03
0.03
0.03
0.16
MBRL-Norm
0.04
0.78
0.74
0.98
0.05
0.68
0.85
0.97
0.05
0.79
0.87
0.98
MBRL-Ours
0.00
0.01
0.01
0.07
0.00
0.01
0.02
0.09
0.00
0.03
0.01
0.10
than Bascline, which validates our hypothesis that COM is not powerful enough to represent causality. To investigate the training procedure, we plot the training objectives in Figure with two different sampling temperatures T, which controls the sampling variance in (0, T). A large temperature provides strong exploration but causes slow convergence. However, we find that using small temperature leads to unstable training with high variance due to poor exploration capability.
How does causality help the generation process? (Q2) The design of the Baseline represents the model that uses the full graph. Therefore, the results in Table also demon- strate that the causal graph is more helpful than the full graph. To investigate the reason why the causal graph helps the learning, we conduct an ablation study on the number of irrelevant nodes (I node), which do not have edges in the causal graph. In Figure 5, we can see that adding more irrelevant vehicles enlarges the gap between CausalAF and Baseline the performance of Baseline gradually drops the number of nodes increases but CausalAF has consistent performance. The reason is that CausalAF is able to diminish the impact of irrelevant in- formation with COM and CVM.
0.75
CausalAF-11 14
Baseline-11
CausalAF 31
Baseline
CausaláF 6-1
Baseline-611
0.50
CausalAF- 11-1
Baseline-11-
CausalAF-164
Baseline-16/
Training Objective
0.00
-0.25
-0.50
0.75
-1.00
100
200
300
400
500
Iteration
Figure 5: The training objectives in the Pedestrian scenario from different num- bers of irrelevant vehicles.
How can we use the generated scenarios? (Q3) Finally, we explore how to use generated safety-critical scenarios. We train 4 RL agents (ISAC, PPO, DDPG, MBRL) under normal scenarios (uniformly sample the parameters of objects in the scenario) then we evaluate them under scenarios generated by four different methods: Normal, L2C, MMG, and Ours (CausalAF) to test the performance under safety-critical scenarios. We also train another 4 agents under scenarios generated by our method (ISAC, PPO. DDPG, MBRL)-Ours) and evaluate under four different scenarios. We report the collision rate in Table 2. We find that scenarios generated by our CausalAF cause more collision to the RL agents, which also shows that training on normal scenarios is not enough for safety. After training on scenarios generated by CausalAF, the agents achieve lower collision in all scenarios, indicating the usefulness of training on safety-critical scenarios.
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5 Related Work
Goal-directed generative models. DGMs, such as Generative Adversarial Networks [17] and Variational Auto-encoder [18], have shown powerful capability in randomly data generation tasks [19]. Among them, goal-directed generation methods are widely used [20]. One line of research leverages conditional GAN [21] and conditional VAE [22], which take as input the conditions or labels during the training stage. Another line of research injects the goal into the model after the training. [23] proposes a latent space optimization framework that finds the samples by searching in the latent space. This spirit is also adopted in other fields: [24] finds the molecules that satisfy specific chemical properties, [25] searches in the latent space of StyleGAN [26] to obtain targeted images. Recent works combine the ad advantages of the above two lines by iteratively updating the high-quality samples and retraining the model weights during the search [27]. [28] pre-trains the generative model and optimizes the sample distribution with reinforcement learning algorithms.
Safety-critich driving scenario generation. Traditional scenario generation algorithms sample from pre-defined rules and grammars, such as probabilistic scene graphs [29] and heuristic rules [30]. In contrast, DGMs [31, 32, 33, 34] are recently used to construct diverse scenarios. Adversarial optimization is considered for safety-critical scenario generation. [35, 36, 37] manipulate the pose of objects in traffic scenarios, [38, 39] adds objects on the top of existing vehicles to make them disappear, and [3] generates the layout of the traffic scenario with a tree structure integrated with human knowledge. Another direction generates risky scenarios while also considering the likelihood of occurring of the scenarios in the real world. [40, 41, 42] used various importance sampling approaches to generate risky but probable scenarios. [34] merges the naturalistic and collision datasets with conditional VAE. [43, 16, 44, 45] learn traffic prior from pre-collected dataset.
Causal generative models. The research of causality [8] is usually divided into two aspects: causal discovery finds the underlying mechanism from the data; causal inference extrapolates the given causality to solve new problems. A toolbox named NOTEARs is proposed in [46] learn causal structure in fully differentiable way, which drastically reduces the complexity caused by combinato- rial optimization. [47] show the identifiability of learned causal structure from interventional data, which is obtained by manipulating the causal system under interventions. Recently, causality has been introduced into DGMs to learn the cause and effect with representation learning. CausalGAN [48] captures the causality by training the generator with the causal graph as a prior, which is very similar to our setting. In CausalVAE [49], the authors disentangle latent factors by learning causal graph from data and corresponding labels. Previous work CAREFL [50] also explored the combination of causation and autoregressive flow-based model and is used for causal discovery and prediction tasks.
Conclusion and Limitation
This paper proposes a causal generative model that generates safety-critical scenarios with causal graphs obtained from humans prior. To incorporate the causality into the generation, we use the causal graph to regularize the generation of the behavioral graph, which achieved by modifying the generating ordering and graph connection with two causal masks. By injecting causality into generation, we efficiently create safety-critics scenarios that are too rare to find in the real world. The experiment results on three environments with clear causality demonstrate that CausalAF outperforms all baselines in terms of efficiency and performance. We also show that training on our generated safety-critical scenarios improves the robustness of RL-based driving algorithms. The proposed method can be naturally extended to other robotics areas since critical scenarios are vital for learning- based algorithms but rare to collect in the real world, e.g., risky scenarios for household robots that involve human interaction.
The main limitation of this work is that the causal graph, summarized by humans, is assumed to be always correct, which may not be true for complicated scenarios. We will explore methods robust to human bias when attaining the causal graph, for example, automatically discovering causal graphs from observational or interventional datasets. Although this work is evaluated in simulations, we believe the autonomous driving area still benefits from safety-critical scenarios with abstracted representation, which shares smaller sim-to-real gap compared directly using raw sensor input.
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Acknowledgments
We gratefully acknowledge support from the National Science Foundation under grant CAREER CNS-2047454 and support from the Manufacturing Futures Initiative at Carnegie Mellon University made possible by the Richard King Mellon Foundation.
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12


Reviews:
[{"review_id": "XikBDe8eUId", "reviewer": "Reviewer_pK7P", "summary": "The objective of this paper is to generate test cases for automated driving systems that present realistic and difficult situations (which are only rarely occurring under generic sampling methods).  The idea is to augment a generative model for sequences of important events with constraints from a causal model, thus generating more plausible scenarios that still result in a high probability of impact and that therefore represent good test problems.", "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": "The problem addressed by the paper is important and the ideas seem sensible.  In particular, this method provides us with a way of taking some human expertise (basic, generic causal structures) in a form that is easy for humans to supply and leveraging it to generate good test scenarios.\n\nOne possible objection is that this work is not too relevant to the field of robotics;  but it is relevant to the extent that automated vehicles are robots and that it is critical to train them on data distributions that exhibit important possible failure modes.   \n\nAn answer to this objection which (I think) would actually make the paper stronger, would be to assert that this work is important to any agent that is being trained via typical learning methods to take actions in a complex domain in which there are seriously risky situations that are relatively rare, and that these situations can come up in a wide variety of robotics applications (including industrial or household robots sharing workspace with humans, or robots working on disaster recovery.)\n\nA primary difficulty with this paper is clarity and organization of the writing.  It is very important to describe, rigorously and early,   exactly what kind of testing data you will produce and how it is used.\n- What exactly is the type of a scenario $\\tau$?  Does it specify detailed trajectories for all the vehicles, stop-lights, etc?   Or all but the agent?\n- How are the scenarios used during reinforcement learning?   Do we use the current RL policy $\\pi$ inside $\\mathcal E$ to generate new scenarios, and then do offline RL in those scenarios to generate a new policy?  \n- Are the constraints from the causal graph imposed *at scenario generation time* or are they somehow incorporated into $\\phi$ so that the underlying autoregressive generation process tends to generate graphs that satisfy them?\n\nHere are some other questions that came up for me as I was reading, which might be addressable by rewriting, taking care to make sure the paper is readable by someone new to your work, defining terms before using them, etc.\n- What does it mean for a graph to \"work as a high-level planner\"?\n- How does the behavioral graph encode the ordering of actions given that there can be parallel self-loops?   How do you guarantee the actions are legal?\n- It would be better to explain the behavioral graph (semantics and use) before talking about how to generate them.\n- Also, explain to us how the behavioral graph will help generate rare-but-interesting scenarios.  (I finally understood this later in the paper)\n- 2.2 Say earlier that G^B is a DAG.\n- Are CG and BG the same type?  What does it mean to minimize distance between them?\n- How can a node be directed?\n- The description of causal visible masks could be clearer.  It \"filters the non-causal information when generating edges\"  But what does it\nmean to do that?\n- Doesn't the likelihood of collision depend on the policy being executed?  I guess you are going to do this dynamically?  Given a\npolicy, generate scenarios that cause crashes, use those scenarios to improve your policy, etc.?\n- It is generally good practice to only put into bold the method(s) that are statistically significantly best or indistinguishable from best (not just with the highest mean)\n- Are these scenarios necessarily interesting if they cause a simple rule-based policy to crash?  But I guess the idea is that this method can be used\nto cause other policies to crash, as well?\n- I like that you put in a pedagogical figure (2) but for it to actually teach, it would need more explanation.\n\nThe study on irrelevant nodes was good and illuminating.\n\nIt would be great to explain more fully the importance of having monotonicity of likelihood.\n\nThis whole framework of auto-regressive graph generation is very cool, and adding causal constraints is a nice idea.   Might there be other kinds of constraints that humans could specify (or \"skeleton\" scenarios) that could also be incorporated in this framework?\n\n-------------------\nAfter discussion, I feel that:\n- the exposition is improved but could probably be made more systematic still\n- the solution really is interesting and feels novel\n- I still don't quite understand what you mean by:\n\"Nodes in behavior graph represent objects we are interested in, e.g., vehicles, pedestrians, traffic signs, traffic lights, etc. Edges in represent the properties of objects, e.g., initial positions, velocities, and colors. Therefore, the behavior graph describes the sequential interaction between objects, which can be viewed as a motion planner.\"\nTo me, a \"planner\" takes some kind of goal or objective and some kind of transition model and does some search to find an action sequence that optimizes the objective.\n\nI will improve my recommendation\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "The ideas here seem interesting but are not really clearly enough articulated for me to have understood the proposed methods well enough for me to evaluate them.  I would encourage a rewrite of the paper.\n", "technical_quality": "Very Good:  Convincing.", "clarity_of_presentation": "Good: Minor revision needed to improve organization or clarity.", "potential_impact": "", "robotics_focus": "Highly relevant to robotics but no hardware experiments", "quality_of_limitations": "Limitations are addressed clearly", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"impact": "3: The work is incremental and unlikely to have much impact, even though it may be technically correct and well executed.", "issues": "I wouldn't ask for any additional work during the revision period.  I think the rewriting required is fairly substantial.", "reviewer_expertise": "2: The reviewer is willing to defend the evaluation, but it is quite likely that the reviewer did not understand central parts of the paper"}, "extra_text": {}}, {"review_id": "VS6CkXF-0NT", "reviewer": "Reviewer_9o2A", "summary": "This paper presents a solution to generating scenarios in an efficient manner (targeted to automated driving, but more generally applicable).  The authors present a means for leveraging causality, in particular causal graphs, in constructing a behavior graph that can serve to instantiate scenarios.  The sample efficiency comes from the behavior graph, which alleviates the need for all combinations of behaviors, even implausible ones, that may occur with standard generative models.", "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": "The paper is well-written, offering a unique take on an important problem of finding rare events and corner cases for AV safety in a principled way.  The presented approach seems to offer a definitive improvement over existing methods in terms of sample efficiency, in cases where causality can be leveraged.  The authors introduce a novel procedure for using AF to construct a behavior graph in generating two types of causal masks: a causal order mask, and a causal visible mask to properly impose causal ordering of nodes and edges.  The authors also include a well-written code artifact, which will certainly boost reproducibility.\n\nOne major weakness of the paper is the rather shallow descriptions motivating the various components, particularly in generating the causal graph and autoregressive flows.  It seems quite a bit counterintuitive that to generate a simulation of a rare event or rare scenario, that the details of such a scenario must already be specified by a human (i.e. the causal graph must be known).  Indeed, in all such scenarios It would be worth elaborating on why such a scheme helps, starting with some example scenarios.\n\nThere is also little background given on the choice of autoregressive flows, and no introduction to normalizing flows.  What are the redeeming properties of autoregressive flows?\n\nSome further questions on the implications of using causal graphs.  For both the causal graph and behavioral graph, do they allow for two-way interactions between agents?  For instance, the case of two vehicles negotiating a merge?  From the definitions given, this does not seem to be the case.  More generally, the authors are strongly encouraged to note any inherent limitations in the causal graph that may make it impossible to form scenarios that may otherwise be possible using causality-free approaches.  Also, the node and edge types are also not clear - what do the authors mean by “type”?  Further explanations in the behavioral graph section (Section 2.1) should be added, and examples should be more complete.\n\nWhile I acknowledge that the authors do address the causal graph requirement as a limitation, I would recommend that authors strongly consider adding an empirical exploration on the diversity of the generated scenarios on a limited set of causal graphs versus the diversity of causality-free methods.  In other words, how much diversity is lost by relying on users to supply a causal graph?", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "Because this paper presents a novel approach to scenario generation, with clear empirical benefits, I would advocate for acceptance.  The algorithmic contributions make for a very strong contribution, as does the code that is released along with the paper. The authors should address the issues brought forth in this review; in particular, by better motivating the use of autoregressive flows and explaining further the limitations of having a causal graph, particularly in loss of scenario coverage (diversity).  Further empirical studies on the diversity issue are highly encouraged.", "technical_quality": "Very Good:  Convincing.", "clarity_of_presentation": "Very Good:  Well organized and clear.", "potential_impact": "", "robotics_focus": "Highly relevant to robotics but no hardware experiments", "quality_of_limitations": "Additional details required", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"impact": "4: The work contains interesting new ideas that will potentially have major impact in robotics or machine learning.", "reviewer_expertise": "4: The reviewer is confident but not absolutely certain that the evaluation is correct"}, "extra_text": {"issues": "1. Addressing what redeeming qualities are for autoregressive flows over other types of normalizing flows, any background on why normalizing flows and its impact on likelihood computation, as this is not explained anywhere.\n2. Regarding causal graphs, what are the limitations in terms of diversity of the scenarios if the user is expected to provide such domain-specifics?  The authors should provide an empirical justification for causal graphs, and improve the discussion on this topic.\n3. The authors should address whether there are inherent limitations in the causal graphs and the generated behavior graphs.  For instance, are bi-directional interactions (one agent influences another, and vice versa) possible or not?\n4. A better background and discussion on behavior graphs and causal graphs.  For instance, better descriptions of what \"type\" means in context, by way of better examples.\n5. How are $V_i$, $E_{i,j}$ initialized in the algorithm 1?\n6. There are a number of grammar mistakes. For instance, inconsistent references to figures (\"Figure X\" vs. \"Fig X\"), and sentence fragments (\"... merges the naturalistic and collision datasets with conditional.\" on line 282)."}}, {"review_id": "RwA0d2ZWHPU", "reviewer": "Reviewer_Gk4u", "summary": "The paper proposes CausalAF, a method to generate safety-critical scenarios by learning the behavior graph given the causal graph. The paper claims dramatic improvements on generating scenarios that meet the objective over data-driven baselines. Finally, they also show that the generated scenarios are beneficial for training RL policies in contrast to random scenario generation.", "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": "### Strengths\n- The introduction captures very well the state of the self-driving industry. Scenario generation is a highly relevant task at the moment towards solving self-driving.\n- The paper is well structured and the manuscript is fairly polished.\n- Representing scenarios in a graphical way makes sense, and learning behavior graphs that satisfy the causal structure is a relevant problem.\n- It is good to see that causality helps the generation process as covered in L238-251.\n\n### Weaknesses\n- Adversarial optimization is not treated as a first-class baseline. This is a constant throughout the introduction, the related work as well as the experiment. However, I believe that with the objective described in L160, methods such as STRIVE, KING and AdvSim (see citations below) would do extremely well. Unfortunately, such comparisons aren't available in the paper.\n- In L82 it says that the edge matrix represents the sequential interaction between objects. I didn't understand what's the sequential part. As far as I understand, the only attrributes getting optimized are the initial position and velocity. This is what I understand from L89.\n- It is not clear what is the exact parameterization/architecture of $\\mathcal{F}_\\phi$. Can it handle a variable number of actors in the scenario? Or a different module needs to be trained for every scenario?\n- Expert knowledge and effort is required to provide the causal graph. While it is interesting to include prior knowledge in the problem, this route seems very time-consuming and that it will not generalize to more complex scenarios. While the paper acknowledges this limitation, I believe it hinders the applicability far too much for this work to be useful as it stands.\n- The scenarios are extremely simple, and the baselines perhaps too weak. In terms of scenario generation, I'd be interested in seeing a comparison against adversarial optimization as well as simple heuristics based on time-to-collision in Table 1. Moreover, in Table 2 the impact of the generated scenarios in training RL policies is only compared to a random baseline, as opposed to comparing to the other baselines for scenario generation.\n- Finally, in the limitations section it is naively stated that the sim-to-real gap is \"almost negligible\". The paper doesn't provide any support for this argument, and I believe is not true.\n\n```\n@inproceedings{rempe2022generating,\n  title={Generating Useful Accident-Prone Driving Scenarios via a Learned Traffic Prior},\n  author={Rempe, Davis and Philion, Jonah and Guibas, Leonidas J and Fidler, Sanja and Litany, Or},\n  booktitle={Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},\n  pages={17305--17315},\n  year={2022}\n}\n@article{hanselmann2022king,\n  title={KING: Generating Safety-Critical Driving Scenarios for Robust Imitation via Kinematics Gradients},\n  author={Hanselmann, Niklas and Renz, Katrin and Chitta, Kashyap and Bhattacharyya, Apratim and Geiger, Andreas},\n  journal={arXiv preprint arXiv:2204.13683},\n  year={2022}\n}\n@inproceedings{wang2021advsim,\n  title={Advsim: Generating safety-critical scenarios for self-driving vehicles},\n  author={Wang, Jingkang and Pun, Ava and Tu, James and Manivasagam, Sivabalan and Sadat, Abbas and Casas, Sergio and Ren, Mengye and Urtasun, Raquel},\n  booktitle={Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},\n  pages={9909--9918},\n  year={2021}\n}\n```", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "While I think the idea has merit, I believe removing the need for the expert-provided causal graphs and making more thorough experiments are a must to accept this paper. The baselines the method is compared against are weaker than they should.", "technical_quality": "Poor: Lack of required evidence to support the claims.", "clarity_of_presentation": "Good: Minor revision needed to improve organization or clarity.", "potential_impact": "", "robotics_focus": "Relevant but unlikely to deploy to hardware in near future", "quality_of_limitations": "Limitations are not well addressed", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"impact": "2: Unsure, difficult to assess.", "issues": "See weaknesses section.", "reviewer_expertise": "3: The reviewer is fairly confident that the evaluation is correct"}, "extra_text": {}}, {"review_id": "OSC4V8s7KU5", "reviewer": "Reviewer_aF4L", "summary": "Although nowadays autonomous vehicles can handle most scenarios, their performance in a small number of safety-critical cases is not evaluated comprehensively. The main reason is that these cases are difficult to collect and thus the number is limited. This paper proposes a new generative method taking causal graphs as input to produce countless safety-critical scenarios, which could help tame the long tail problem and help improve the safety of ADS. Extensive experiments are conducted to verify the effectiveness the proposed method.", "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": "**Strength**:\n1) This paper proposes a new graph-based scenario description tool so that causality could be integrated\n2) The idea of generating scenarios from a causality graph is original and interesting\n3) It seems that the authors give a solid convergence guarantee, based on the delicate notation. But I am not an expert at the graph model, and thus can not ensure the correctness of the modeling.\n4) The experiment is complete, including baseline comparisons, ablation study (on COM and CVM) and RL experiments.\n\n**Weakness**:\nThe weakest part of this paper is that the experiment setting should be made more clear and some qualitative results should be added. \n\n1) What do the scores in Table 1 mean? Is it the collision rate of the generated case?\n2) What do the generated scenarios look like? Some qualitative results should be visualized to show the diversity of generated scenarios.\n3) Are there only 3 synthetic maps? If not, please describe how many maps are contained in these simulators and how do they look like, since the map structure will greatly influence the generated scenarios. If these maps are synthetic, I would like to know if there are any future plans to extend this method to real maps, which are more complex and unstructured\n4) The pre-defined types of nodes and edges used in the experiment should be made clear\n5) In the RL experiments, are the safety-critical cases split into training and test sets? \n\n\n\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "I think the weakness mentioned above is easy to solve in revision. Therefore, I would like to give a weak acceptance.", "technical_quality": "Very Good:  Convincing.", "clarity_of_presentation": "Good: Minor revision needed to improve organization or clarity.", "potential_impact": "", "robotics_focus": "Relevant but unlikely to deploy to hardware in near future", "quality_of_limitations": "Additional details required", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"impact": "4: The work contains interesting new ideas that will potentially have major impact in robotics or machine learning.", "issues": "See weakness", "reviewer_expertise": "3: The reviewer is fairly confident that the evaluation is correct"}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)