DiffLight: A Partial Rewards Conditioned Diffusion Model for Traffic Signal Control with Missing Data
Authors: Hanyang Chen
Yang Jiang
Shengnan Guo
Xiaowei Mao
Youfang Lin
Huaiyu Wan
Venue: NeurIPS 2024 spotlight (2024)
Keywords: Traffic signal control
Reinforcement learning
Diffusion model
Spatial-temporal data
Primary area: machine_learning_for_other_sciences_and_fields
TL;DR: We propose DiffLight, a conditional diffusion framework, unifying traffic data imputation and decision-making for TSC with missing data.

Abstract: The application of reinforcement learning in traffic signal control (TSC) has been extensively researched and yielded notable achievements. However, most existing works for TSC assume that traffic data from all surrounding intersections is fully and continuously available through sensors. In real-world applications, this assumption often fails due to sensor malfunctions or data loss, making TSC with missing data a critical challenge. To meet the needs of practical applications, we introduce DiffLight, a novel conditional diffusion model for TSC under data-missing scenarios in the offline setting. Specifically, we integrate two essential sub-tasks, i.e., traffic data imputation and decision-making, by leveraging a Partial Rewards Conditioned Diffusion (PRCD) model to prevent missing rewards from interfering with the learning process. Meanwhile, to effectively capture the spatial-temporal dependencies among intersections, we design a Spatial-Temporal transFormer (STFormer) architecture. In addition, we propose a Diffusion Communication Mechanism (DCM) to promote better communication and control performance under data-missing scenarios. Extensive experiments on five datasets with various data-missing scenarios demonstrate that DiffLight is an effective controller to address TSC with missing data. The code of DiffLight is released at https://github.com/lokol5579/DiffLight-release.

DiffLight: A Partial Rewards Conditioned Diffusion Model for Traffic Signal Control with Missing Data
Hanyang Chen 1.2 Yang Jiang!? Shengnan Guo Xiaowei Mao
Youfang Lin 12, Huaiyu Wan
School of Computer Science and Technology, Beijing Jiaotong University, China Beijing Key Laboratory of Traffic Data Analysis and Mining. Beijing, China (hanyangchen, jiangyang, guoshn, maoxiaowei, yflin, hywan]&bjtu.. edu.
Abstract
The application of reinforcement learning in traffic signal control (TSC) has been extensively researched and yielded notable achievements. However, most exist- ing works for TSC assume that traffic data from all surrounding intersections fully and continuously available through sensors. In real-world applications, this assumption often fails due to sensor malfunctions or data loss, making TSC with missing data a critical challenge. To meet the needs of practical applications, we introduce DiffLight, novel conditional diffusion model for TSC under data- missing scenarios in the offline setting. Specifically, we integrate two essential sub-tasks, i.e., traffic data imputation and decision-making by leveraging Par- tial Rewards Conditioned Diffusion (PRCD) model to prevent missing rewards from interfering with the learning process. Meanwhile, to effectively capture the spatial-temporal dependencies among intersections, transFormer (STFormer) architecture. In addition, we propose a Diffussin Com- munication Mechanism (DCM) to promote better communication and control performance under data-missing scenarios. Extensive experiments on five datasets with various data-missing scenarios demonstrate that DiffLight is effective controller to address TSC with missing data. The code of DiffLight is released at atttps://githbb ggt.ha..ccm//ooolll/9///f/ffff.. release
design
Introduction
With the acceleration of urbanization, the surge in the number of vehicles in cities has led to increas- ingly severe traffic congestion and pollution problems []] Intersections, where traffic congestion often occurs, become key in addressing these problems. To this end, solving the traffic signal control (TSC) problem is crucial for reducing traffic congestion in intersections by controlling traffic lights. Over the years, many approaches have been developed to tackle the TSC problem, which can be categorized into conventional approaches and reinforcement learning-bar based (RL-based) approaches. Conventional approaches, like Fixed-time (2). SCOOT (3] and SCATS [4) have been widely deployed in different cities. However, these approaches struggle to adapt to the inherent stochasticity and highly dynamic nature of real-time traffic conditions, limiting their effectiveness in responding dynamic traffic demands.
Recently, reinforcement learning (RL) is introduced into TSC to enable adaptive traffic signal control 5. 7 8 9 [TO] 12 [13. Unlike conventional approaches, RL-based approaches for TSC deploy learnable agent each intersection, allowing traffic signals to be adjusted dynamically based on real-time traffic conditions. However, most existing RL-based approaches for TSC assume that traffic
"Corresponding author
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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data from all surrounding intersections is fully and continuously available through deployed sensors. In practice, this assumption is often unrealistic. Due to budget constraints, not all intersections can be equipped with sufficient sensors. Even if necessary sensors are deployed, malfunctions or errors could lead to incomplete data collection. Therefore, the research on TSC with missing data is more in line with the needs of actual scenarios but has not been studied sufficiently yet.
Furthermore, existing RL-based approaches for TSC can be categorized into two types, i.e., online approaches and offline approaches. Most RL-based approaches for TSC rely on the online setting, interacting with the environment frequently. Specific to data-missing scenarios, MissLight [14] composed of the traffic data imputation stage and decision decision-making stage has been proposed in the online setting. However, frequent interaction with the and potentially unsafe, especially when dealing with incomplete data. As an alternative, training using offline traffic data with missing values offers a safer and more practical solution. Therefore, we focus on the offine setting in this paper. Similar to the online setting, traffic data imputation and decision- maaiin for TSC with missing data are two sub-tasks we must confront in the offline setting.
traffic environment is challenging
Recently, diffusion models [5] have been introduced into offline RL due to their powerful generative 19 20). These approaches frame sequential decision-making as conditional generative modeling and utilize the generative ability of the diffusion model to capture complex policy distribution offline datasets to make better decisions. Additionally, in the context of TSC with missing data, traffic data imputation is equally critical. Inspired by existing works [21 22, (23) we approach traffic data imputation as a conditional generative problem, similar to decision- Considering the similarity of the two sub-tasks, we propose to unify traffic data imputation and decision-making for TSC with missing data by utilizing the powerful generative ability of the diffusion
ability [66 17
model.
There are several challenges that must be addressed to integrate the two sub-tasks mentioned above effectively. Firstly, in RL-based approaches for TSC, rewards which are typically vehicle queue length, are critical for the performance of controllers. However, due to the absence of traffic data, only partial rewards are available. A straightforward solution might be to fill in the missing rewards with padded values, which could confuse the imputed rewards with the actual ones, leading a negative impact on performance. Secondly, relying solely on traffic data of the local intersection makes it challenging to capture the dynamic and spatial-temporal dependencies in the traffic network for traffic data imputation and decision-makin broader context, as traffic data from the local intersection may not adequately reflect the behaviors and interactions occurring across the entire network. The absence of traffic data from neighboring intersections may further exacerbate this issue, hindering the ability to capture these dependencies and potentially leading to a decline in performance.
tasks. The complexity of traffic flow often requires a
To tackle these challenges, we introduce DiffLight, a novel conditional diffusion model for TSC with missing data. We propose a Partial Rewards Conditioned Diffusion (PRCD) model for both traffic data imputation and makingg under data-missing scenarios to prevent missing rewards from interfering with the learning process. Meanwhile, to effectively capture the spatial-temporal dependencies among intersections, we design the noise model as a (STFormer) architecture. In addition, we propose Diffusion Communication Mechanism (DCM) to enable communication and promote the capture of spatio-temporal dependencies in the traffic network through the propagation of generated observations, facilitating better control in scenarios with missing data. Extensive experiments on five datasets with various data-missing scenarios are conducted to evaluate the effectiveness of DiffLight. The experimental results indicate that DiffLight is highly competitive for TSC with missing data.
transFormer
2 Preliminaries
2.1 Partially Observable Markov Decision Process
We consider partially observable Markov decision process (POMDP) in the offline setting, defined
as tuple A, P, R, 2, 7). S is the state space, and 8, E S denotes the state at time l. A is the set of available actions and a, E A denotes the action of an agent at time L. The observation or E Ω observed by the agent part of the state 8 and can be derived from the function ((x)). r, = R(s,) is the immediate reward of agent at time t. P and y denote the transition probability function
2

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and the discount factor separately. The optimization objective is to learn a policy и for agents to maximize the expected return Es....[R,) where R, ExTTr.
2.2 Traffic Signal Control with Missing Data
We formulate TSC with missing data as POMDP, and consider TSC in traffic network with several intersec- tions. Agents are deployed at each intersection traffic network. As illustrated in Figure 1 for a four- way intersection, there are twelve traffic movements from the intersection's 's entrance lane lin to the departure lane hout. and four pairs of traffic movements without con- flict comprise four traffic signal phases, i.e., A, B, C, D. For example, the traffic signal phase of the intersec- tion in Figure i is phase-A which involves movement-2 -12 + put. in 11 ouu im 12 In
the
+ out: 12t + 19 } and movement-8
13
In this paper, the observation On contains the number of vehicles /mum and queue length Lqqeue in every entrance lane of the local intersection. Available actions are four phases. The immediate reward re is defined the sum of the queue length Ei,,. Lquene- Due to the lack or error of sensors resulting in missing traffic data, Og and Tt. which are derived from traffic data, could be missing in a particu- lar missing pattern. We consider random missing and kriging missing patterns detailed in Appendix To simplify the problem, we assume that and ra in an intersection are missing simultaneously.
Figure 1: Illustration of four-way way inter- section with 12 traffic movements and 4 traffic signal phases.
2.3 Diffusion Models for Reinforcement Learning
Diffusion model. Diffusion models [5 24 25 powerful generative model, provide frame- work to model the data generative process as a discrete difftusion process. Diffusion models consist of two processes: the forward process and the reverse process. In this paper, the forward process is de- fined as q(** -1) == N (V11- 3 II) by the Markov process, where 3* is the variance of the noise at timestep k. We adopt DDIM sampler (24) to sample in the reverse process in order to ac- celerate sampling. DDIM sampler is parameterized with pe (2* 1 x=*) x²)) == N (uo(" k), 2I)..
which can be optimized by simplified surrogate loss,
(( := B..- k) - cc
The reverse process begins by sampling an initial noise Jæ -N(O,)) I). The estimated mean of Gaus-
sian (1 k) v T + /1 a+- -lee(aa k) where io va v1 afc (x k)).
a = gh, a II a and ca(x k) is predictor used estimate noise.
Diffusing decision-making Recently, many diffusion-based approaches have been proposed to address decision- problems in RL. Among existing works, Diffuser [16) chooses to diffuse on an observation-action trajectory with returns as the condition to generate actions directly. Decision Diffuser [[6] focuses solely on diffusing the observation trajectory conditioned on returns. By avoiding direct diffusion over actions, Decision Diffuser enhances performance in scenarios with discrete actions. In this paper, considering the discrete nature of actions in TSC, we focus on introducing the approach diffusing on the observation trajectory sampled from offline dataset D. We denote the k-step denoised output of the diffusion model as (T). The observation trajectory would be diffused to generate 0++1- However, only diffusing on observation trajectory is not enough to make decisions. An inverse dynamics model f is adapted to generate the action a, that makes the observation transit from o, to 0c+1,
a1 fo(or,
(2)
3

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Classifier-free guidance. Classifier- free guidance 26 aims to learn the conditional distribution ((x(T)y((7)) It learns both conditional 6g(2* (T).3(T)) (. k) and an unconditional eg ca (T). k) for the noise. Then, the perturbed noise (T)) o, k) + ((e((=(T))
- co (T),
can be used to generate samples, where w is the guidance scale.
3 Methodology
In order to effectively unify traffic data imputation and decision- makinn for TSC with missing data, we consider both of them as a conditional generative modeling problem via diffusion models,
max Ey Pa (x (**(())
8
where pa is a learnable model distribution to estimate the conditional data distribution of trajectory x² (r), conditioned on (T)). We construct generative model according to the conditional diffusion process,
q( (T) -
po(=~~1 (T), (T),
(4)
with conditions as,
y(T) :- (-))=Ir(() (
5((T) : [Tohs Thail-
(5)
To facilitate better understanding of the symbol definitions, we categorize the trajectory segments into three types. The observed trajectory consists of data collected by sensors up to time t. The missing trajectory includes data that have not been collected during this period. The observable trajectory encompasses both the observed trajectory and the data that could potentially be collected in the future. In this context, r(r) is the observable reward trajectory, and Tobs is the observed part of trajectory from the local intersection. T UN UNeinniir7 is the observed observations from neighboring intersections, where T' denotes the observation trajectory of the neighboring intersection .N is total number of neighboring intersections, fnei(-) (-) represents the observed observations from entrance lanes of all neighboring intersections that feed into the entrance lanes of the local intersection, as shown in Figure Due discrete and on observations and utilize the inverse dynamic model to generate actions, which demonstrates a We define the observation trajectory t under
actions in TSC, choose to diffuse solely
better performance proven in Appendix FT and F.6 data-missing scenarios as,
= 00- Ōz, 0,+1, ... H++H]:
(6)
where is the observation collected by sensors, o, is the uncollected observation up to time t or potentially collectible observation in the future, the horizon of future observations. It should be noted that we generate H-step future observations to enable effective long-horizon planning [16].
the length historical observations and // is
Figure 2
shows the overview of DiffLight, which consists of the Partial Rewards Conditioned Diffusion (PRCD), a noise model with Epatial-Temport transFormer structure (STFormer), and the Diffusion Communication Mechanism (DCM). We introduce each of them in the following sections.
3.1 Partial Rewards Conditioned Diffusion
Under data-missing scenarios, sensors deployed to collect traffic data for rewards may malfunction be lacking. The absence of partial rewards makes it challenging to calculate returns. Therefore, we adopt partial rewards the condition instead of returns [16 17 19 which can be expressed as,
r(T)
Fe..t4 rt+H]:
where rt the collected reward or a potentially collectible reward the future, and Ft is the uncollected reward.

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E-
Faet
(*(
v(t)
Crasing
STFormer
MLP
MLP
Communicaion
Trafffic
Data
DCM
Temporal Self-Antation
Spotial
Self-Arscnion
Partial Rewards Conditiuned Diffusion (PRCD) with STFormer
Otomatiee
Inverse Dynamies
Figure 2: An overview of DiffLight. We demonstrate the signal control process of an intersection in random missing. Traffic data is collected by sensors to derive rewards and observations. Missing rewards and observations observable rewards from the local intersection, and observation trajectories from neighboring inter- sections would be input into PRCD with STFormer. In the inference process, DCM would work with STFormer to generate observations. The inverse dynamics model is used to generate actions to control the traffic signal.
masked. Only the observed part of the observation trajectory and
There are two ways to handle the missing part of rewards: conditioning on the rewards with padded values or conditioning missing part is feasible way. However, padded values could confuse the imputed rewards with the actual ones, leading decision-makee we choose to condition on only partial observable rewards. We assume that the observable part and the missing part of the trajectory are collected by real sensors and virtual sensors separately, and the distribution of traffic data collected by two kinds of sensors is independent. In this case, the distribution in Equation 3 can be factorized as,
the partial observable rewards directly. Padding specific value in the
negative impact performance proven in Section 4 For better
Po ( (T)) = (=e (( pe pe(x (Tmis) (T/mi))l/((T)
(8)
where Tobs is the observable part of the trajectory from the local intersection, and Tmis is the missing part. We parameterize Equation as the same form of locally conditioned diffusion (27 28).
propose partial rewards conditioned diffusion (PRCD) with classifier-free guidance (26) and introduce it into TSC with missing data. Given condition set = {Ø, r(T)} and binary non-overlapping mask set mmiis Mobs). J. PRCD assigns partial rewards to corresponding observation sub-trajectory masked by m, which can be formulated as,
Co(x* y/ (T), m) : Eo (x (T), k. ('),
(9)
Mimis 2 (a (T), (T),0),
where é0(x* k, ('T),, could be expressed using classifier-free guidance,
(o(x"(T), k. (z)
(10)
w(eo(x* (T), k // (T) -) (T), (3
where &
We provide derivation for the feasibility of PRCD in Appendix E
3.2
Diffusing with Spatial-Temporal Transformer
The noise model with U-Net structure widely applied image generation control [16] 17 19 and other fields. However, it is hard to be applied to capture the spatial-temporal
15
24
29
30
5

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dependencies in TSC. The emergence of Transformer [3]] and its applications on spatial- -emporal
modeling [32 33 34 35 provide promising solution deal with it. In this section, we design Spatial-Temporal transFormer (STFormer) structure to effectively model the spatial-temporal dependencies in TSC, which includes a data embedding layer, stacked I. spatial-temporal encoder layers, and an output layer. Data embedding layer embeds different inputs into embeddings, including diffusion timestep, trajectory timestep, rewards, trajectory of the local intersection, and neighboring intersections. Seatial-Temporaa Encoder layer (STE) is composed of Communication Cross-Attention module (CCA), Spatial Self-Attention module (SSA), and Temporal Self- Aelf-Attention module (TSA). CCA is designed to capture the spatial-temporal dependencies between the local intersection and neighboring intersections. SSA and TSA are designed to capture the spatial dependencies and temporal dependencies at the local intersection separately. Output layer is used to convert the output of STE into the noise we desire to predict. We detail the structure of STForme in Appendix B.2
3.3 Diffusion Communication Mechanism
Observations of neighboring intersections are crucial for TSC with missing data [4]. However, due to the possible absence of observations from neighboring intersections, the traffic signal could be controlled ineffectively. For instance, assume an extreme situation where there is no available observation in both the local intersection and neighboring intersections. In this case, observation trajectories of intersections are all masked by noise, leading to difficulty in decision-making at the local intersection. Therefore, we propose a Diffusion Communication Mechanism (DCM) to disseminate observation information generated by the noise model in the reverse process among intersections, Formally, we formulate DCM as,
UN fnei (T')
k= K, (f) Vak ((
nel
(11)
UN fneil
k< K.
The reverse process begins by inputting original observations of neighboring intersections with missing data. During diffusing, we predict (T'), which is the same in Section 2.3 With the help of DCM, generated observations of neighboring intersections could be spread from neighboring intersections for better decisions of the agent the local intersection. Note that we train our model with ground-truth values collected from neighboring intersections and only use DCM in the inference process.
3.4 Training and Inference of DifTLight
Training process. Given an offline dataset D which consists of observation trajectories, rewards and actions, we train the reverse process pe parameterized through the noise model ep, and the inverse dynamics model fe in DiffLight with the following loss,
((0) :- -E(o, - ff (er.p
(12)
B)r(T))rrr))) + Bb, m) eel?]
For each trajectory т, we sample noise e ~ .N I) and a diffusion timestep & ~ 21(1, K). construct a masked noise array of observations (²) with Toke. and predict the noise (a(a*(T), (T), m). Missing values condition The are padded with zeros. should be noted that we ignore the rewards condition r(T) with probability and the inverse dynamics is trained with individual transitions without missing observation or o'. For the training process of DiffLight, due the inaccessibility of the ground-truth of missing data, we consider it self-supervised learning. In random missing, given a trajectory т and conditions, we can separate the observed part into two parts and set one of them to miss. In kriging missing, randomly mask the whole trajectories of one observed intersection. Then, we can train the noise model ég by solving Equation
Inference process. DiffTLight deployed to every intersection in the traffic network in the inference process. Given rewards r r(T), C'-step observed trajectory of local intersection T' with missing

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data and trajectories of neighboring intersections neei the agent can impute the missing observations of local intersection, predict the observations the future and generate next action with Equation 2 and T0 In order to sample high reward trajectory, the rewards from time / to / + H are considered r(T), which is set 1.
Experiments
4.1 Experimental Setup
Experiment Settings We conduct experiments CityFlow [36], traffic simulator widely used in various RL-based methods. Similar to existing work in 13 we set the phase number as four and the minimum action duration 15 seconds.
Datasets The datasets consist of two parts: offline datasets with missing data and real-world traffic flow datasets with traffic networks. We apply five real-world traffic flow datasets [9] (37 for comparison, including Hangzhou, (Pizz) Hangzhou, (Pizz). Jinan; (Djx), Jinany (Dix and Jinang (D Corresponding offline datasets composed of training trajectories of three online methods. We detail the datasets in Appendix C.. To simulate data-missing scenarios, we adopt masks of different missing rates in different missing patterns, including random missing (RM) and kriging missing (KM), to mask observations and rewards. We describe the details of two patterns and missing Appendix C.2
Evaluation Metrics We use the average travel time (ATT) as the main metric for evaluation, which is widely used evaluate the performance of TSC. It calculates the average time all the vehicles spend between entering and leaving the traffic network during simulation, which is formulated as,
1
ATT
Σ (g)
(13)
where N is the total number of vehicles entering the road network, and t are the entering time and leaving time for the i-th vehicle respectively. The lower ATT indicates a better control performance.
and offline ap- Diffuser [I6]. Decision Diffuser (DD) [77. Similar to the existing work in [14), adopt soor-aadd-forward method (SFM) [42). a rule-based method that has generally more stable performances, to impute missing observations and rewards for these approaches. We detail these approaches and SFM in
Compared Methods We compare our method with Behavior Cloning (BC)
38
proaches, including CQL 33), TD3+BC [40], Decision Transformer (DT)
41
Appendix D
4.2 Performance under Data-Missing Scenarios
train and test our method on all five datasets with different missing patterns and missing rates, and compare our method with all baselines. DiffLight performs the best most of the datasets. We analyze experiments of different missing patterns below.
Random missing. In random missing, we can see that DiffLight achieves optimal or sub-optima performance compared with baselines in all datasets in Table Diffusion- based approaches, including Diffuser and DD, show a better performance than other baselines in most datasets. These diffusion- based approaches utilize noise model to predict noise and generate actions or observations, which helps mitigate the disturbance caused by imputed observations and rewards during the diffusion process. Compared with diffusion-her diffusion process is disturbed by imputed observations and rewards more seriously.
approaches, the performance of other baselines without the

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Table Comparing ATT for Diff and baselines in random missing. We report the mean and the standard error for three trials.
Dataset
Rate
BC
CQL
TD3+BC
DT
Diffuser
DD
DiffLight
10%
349.59
363.5
337.54
300.64
290.66
289.38
286.17110877
Diz
30%
350.08
368.53
338.21
315.64
302.39
298.67
292.81 +0.66
50%
357.13
383.67
343.23
343.96
313.68
422.5
304.71+2.12
10%
382.45
353.23
370.16
347.25
346.82
347.77
327.13
Diz
30%
388.73
352.55
376.06
360.59
366.24
364.6
330.68-12.66
50%
387.77
367.38
375.32
377.79
398.23
395.61
333.90:12.67
10%
320.6
299.07
315.54
308.78
272.51
260.76
272.18110.93
JN
30%
328.97
310.8
326.37
377.39
295.09
300.49
279.10+2.10
50%
355.47
322.25
351.2
439.89
324.75
517.99
290.02+2.18
10%
288.42
305.86
322.44
259.3
255.12
245.85
247.17+
D
30%
297.26
308.13
330.43
263.24
271.53
256.16
254.87+-0.6
50%
299.44
320.17
334.78
278.22
302.28
275.2
268.29
10%
301.35
291.26
281.75
257.66
246.90
242.56
246.65
30%
315.03
295.61
283.24
312.56
258.83
256.95
254.55:10.3.
IN
50%
326.55
301.1
292.98
382.93
272.36
351.92
265.76+00.1
Kriging missing. In kriging missing, DiffLight shows the best performance in most datasets in Table Unlike the results of random missing, DD does not perform well in kriging missing compared with other baselines. Since DD must impute missing observations with the SFM model first, generate future observations with the diffusion model, and then use the inverse dynamics to generate actions, which leads to serious eтrоr accumulation. While other baselines generate actions directly, requiring only roughly imputed observations and rewards.
Table Comparing ATT for DiffLight and baselines in kriging missing. We report the mean and the standard error for three trials.
Dataset
Rate
BC
CQL
TD3+BC
DT
Diffuser
DD
DiffLight
6.25%
338.33
317.69
332.80
300.78
302.99
395.54
294.18 1.3.66
12.50%
346.83
317.94
332.43
310.37
305.93
483.47
294.1111..34
Hz
18.75%
350.08
319.18
333.24
306.35
307.22
572.56
300.3111.31
25.00%
354.86
328.83
341.89
381.94
328.79
836.46
302.16+1.223
6.25%
380.18
354.08
374.04
347.53
363.69
370.80
330.40:10.11
12.50%
375.93
361.52
374.66
363.5
378.51
424.99
319.1147.19
Drz
18.75%
380.74
362.82
376.48
374.69
413.48
435.13
327.61 1-9.68
25.00%
413.46
418.97
390.75
492.56
378.54
590.69
351.21
8.33%
319.85
302.35
317.17
306.52
332.44
595.34
280.75.10.11
D
16.67%
339.19
343.16
349.72
380.97
349.74
643.48
306.06 144.89
25.00%
392.91
398.66
391.32
432.56
410.5
995.99
329.67+16.04
8.33%
287.29
306.94
319.4
261.98
259.51
460.22
254.13
D2
16.67%
299.41
314.43
321.88
267.67
270.15
731.49
272.76+
25.00%
314.63
359.33
323.65
295.59
295.21
1049.19
325.20++66663
8.33%
310.44
287.25
282.46
368.2
267.64
324.42
249.48-L0.16
D
16.67%
327.7
311.89
295.07
322.96
294.27
399.67
274.13
25.00%
381.37
337.33
312.44
494.04
292.26
409.76
342.07
We provide overall performance of DiffLight and baselines without missing data as well, which detailed in Appendix F.T In addition, we provide further experiments on the influence of unobserved
locations of intersections scalability of the approach in Appendix F4
Appendix F2 the limit of missing rates in Appendix F3 and the

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4.3
Ablation Study
We further evaluate the effectiveness of different parts in DiffLLight with the following variants. (1) U-Net: this variant replaces STFormer with U-Net as the noise model and missing rewards input are cero-padded. (2) STFormer: this variant uses STFormer as the noise model and keeps missing rewards zero- paro-ppdded. (3) STFormer+PRCD this is equal to DiffLight which uses STFrrmm as the noise model and is conditioned on partial rewards. It should be noted that DCM is adopted in both STForme and STForme++PRCI and all missing observations would not be imputed by the SFM model but are masked with Gaussian noise in order to inpainted in the reverse process in ablation experiments.
Table 3: Ablation study on Hangzhou, and Jinan
Dataset
Pattern and Rate
U-Net
STFormer
STFormer+PRCD
RM (50%)
668.38 65.54
350.60
304.71++2.12
DHz
KM (25%)
363.80 963.80-44.66 44.65
318.21+5584
302.16+11.23
RM (50%)
509.64 41.115
374.41+3.61
290.02-t22.18
D
KMM (25%)
354.90-65.10
374.23-690
329.67+11.044
Table 3 shows the comparison of these variants on Hangzhou, and Jinan; with random missing and kriging missing. Based on the results, we can find that STFrrme which takes spatial-temporal dependencies into consideration leads to great performance improvement over U-Net. It shows that capturing spatial-temporal dependencies important TSC. STFormer+PRCD performs better than STFrrmer, indicating that padding values in rewards could be confused with the ground-truth rewards and only conditioning on partial rewards could have a better performance. Due to the space limitation, we provide further experiments on DCM in Appendix F.5 and the inverse dynamics in Appendix F.6
4.4
Model Generalization
104
1.00
1.00
0.99
630%
1.00
1.02
1:11
1.22
15
1.00
1.06
1.06
16.7% 8.33%
1.00
0.99
1.12
5372 3328
1.00
1.00
1.00
1.02
30%
1.02
506
1.01
1.01
1.00
50%
1.01
1.00
1.00
23.00%
1.03
0.90
1.00
39%
1015h
10%
30%
50%
16.57%
25 69%
(a) Di2:
RM
(b) Dzz: KM
(c) D RM
(d) Dix: KM
Figure 3: The relative generalization performance of DiffLight different missing rates. The x-axis is the missing rate during testing and the y-axis is the missing rate during training. The formula used to calculate the relative generalization performance is depicted below.
We evaluate the generalization performance of DiffLight on Hangzhou, and Jinan, with different missing rates. We train method in specific missing rate and test it on the same dataset with other missing rates. To better compare the generalization performance among models trained in different missing rates, we formulate the relative generalization performance as,
Pr P Pg/Po
(14)
where P. the relative generalization performance of the current missing rate, Pe is the performance of the model trained in other missing rates, and P. is the performance of the model trained in the current missing rate. The results in Figure demonstrate that the generalization performance of iiht is excellent in most situations. If we train DiffLight in high missing rate and test it in lower missing rate, the performance of DiffT.ight remains stable. In contrast, if we train DiffLiight in low missing rate and test it in a higher missing rate, the performance of DiffLight would decrease

---

slightly. As data with higher missing rate has more complex missing situations, making it difficult for models handle these situations.
Related Work
Traffic Signal Control TSC approaches can be categorized into conventional and RL-based methods. Conventional approaches like Fixed-time (2). SCOOT [3] and SCATS [4] have been widely deployed in different cities. In recent years. RL-based approaches for TSC get more attention. DQN algorithm is introduced into TSC in 6 7 for dynamic real-time control. Attention mechanisms applied promote inter-agent communication [9] and build universal models [10). Max- Max-pressure [8] and advanced-MP 13] are proposed to promote the performance of existing methods. TSC with missing data is considered with the help of the imputation model in the online setting. However, there is no existing work to solve this problem in the offline setting.
Diffusion-based Reinforcement Learning There are various works applying the diffusion model to offline RL recently. Diffusion and deep q-learning are combined [18], demonstrating the potential of diffusion in RL. The state-action trajectory is encoded in latent space [43), enhancing credit assignment and reward propagation. In addition to methods relying on TD-learning, Diffuser [16] and Decision Diffuser (17 are proposed as planners to generate the trajectory with a conditional diffusion model. However, they are all studied under scenarios without missing data, while we model TSC with missing data.
Traffic Data Imputation With the development of deep learning, RNN-based methods 44 45 46
show good performance for traffic data imputation. In subsequent studies, diffusion models are utilized to learn the complex distribution in traffic data 21 22]. For TSC, store-and-forwanl method (SFM) 42 is proven have a more stable performance than neural networks [1]. In this paper, we adopt SFM to impute observations and rewards for baselines.
6 Conclusion and Limitation
Conclusion In this paper, we introduce DiftLight, a novel conditional diffusion model designed for TSC in scenarios with missing data. Our approach centers the Partial Rewards Conditioned Diffusion (PRCD) model, which addresses both traffic data imputation and secision-making in the presence of incomplete data. This model helps prevent missing rewards from disrupting the learning process. We address the challenge capturing spatial-temporal dependencies across intersections by designing a
transFormer (STFormer) architecture as the noise model. Additionally, to enhance communication and control performance, we propose Diffusion Communication Mechanism (DCM) that facilitates the propagation of generated observations. We conduct extensive experiments on different datasets and settings to demonstrate that DiffLight is an effective controller to address TSC with missing data.
Limitation In this work, we only consider two missing patterns: random missing and kriging missing. While in the real world, the missing pattern in the traffic network is more complex. Meanwhile, we just adopt SFM which is similar to k-nearest neighbor (KNN) to impute the traffic data for baselines. could lead to the short-sightedness of agents. Future work could explore the influence on performance in more different missing patterns even mixed missing patterns, adopt more different imputation methods, and find out a more far-sighted method to control the traffic signals under data-missing scenarios.
addition, our approach conditioned on partial rewards instead of returns which
Acknowledgments
This work was supported by the National Natural Science Foundation of China (No. 62372031).
10

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A
Broad Impacts
Our proposed method demonstrates effective abilities in TSC with missing data. It can handle different missing patterns and different missing rates when controlling traffic signals. Even in intersection where there are no observed neighboring intersections, DiffLight can perform competitively against baselines with SFM. Moreover, fast inference speed with fewer sampling steps stable performance indicates that DiffLight can be deployed to achieve real-time control in the real world. However, a potential negative impact of this work is that bad decisions could lead to collapse in the traffic network.
B
The Details of DiffLight
B.1 Hyperparameters of DiffL.ight
In this section, we describe the details of hyperparameters,
We set the batch size 64 and each sample contains the trajectory of the whole intersections in the
traffic network. We train model using Adam optimizer [4 with 2e learning rate for 1.5e train steps.
We train Ligh on NVIDIA GeForce RTX A5000 for around 15 hours and test it on the same GPU.
We choose the probability p of removing the condition information be 0.25 and guidance scale a 1.2.
In DiffT.ight we choose the length of historical observations C' = and the planning horizon of observation trajectory H = 3.
We use 100 diffusion steps.
B.2 Structure of STFormer
STFormer is composed of data embedding layer, stacked L spatial-temporal encoder layers, and output layer. We detail cach of them follows.
Data embedding layer. Different inputs are embedded into embeddings e with the same dimension D by the data embedding layer which consist of separate MLPs f'LLP (-).
ea: fk)r((k) eu fMLL((orT-1), e;:= foar(((()))
(15)
Ects : ('ALP(x"(T)) entr == faaLP(Tre))
where lo:r-1 is the timestep of trajectory, Edt, ets. Cr, Eetr and entr represent embedding of diffuusion timestep, trajectory timestep, rewards, trajectory of local intersection and partial trajectory of neighboring intersection separately.
Spatial-temporal encoder layer.
The spatial-temporal encoder layer, abbreviated as STE, is composed of Communication Cross-Attention module. Spatial Self-Attentin module and Temporal Self-Attention module. We adopt the vanilla attention operator [BI] in modules, represented notations are used formulate attention modules. For the embedding of local intersection's trajectory eety xXxLxD where is the number of entrance lanes, the slice is ectr E R LxD and the / slice is e ? For the embedding neighboring intersections' partial trajectories entr E R_=(T-L'')x where L' the number of neighboring intersections' entrance lanes taken into consideration, the slice ei E (T--///)x
fAuiQ, K, V). The following slice
The Communication Cross-Attentin module, abbreviated CCA, is designed to capture the temporlltempora dependencies between the intersection and neighboring intersections. As illustrated Figure | ehi contains information of entrance lanes from neighboring intersections feeding into lane l. This module can be formulated as,
feca (eain elit) = (eiii eii ei
(16)
n:: Ear = SCCA (eilir d: Cmir) + e
(17)
The Spatial Self Self-AAtention module, abbreviated as SSA, and Temporal Self Attention module, abbreviated as TSA. are designed to capture the spatial dependencies and temporal dependencies separately in the local intersection, which can be formulated
14

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fll ISSA (e (eari Cetr: ear) STSA (eaa)) Getrr
Getrr estr)
(18)
Therefore, the spatial-temporal encoder layer be expressed as,
(ett Catr) == fMLL (fss)(eett)) + (estr) + Ectr
(19)
To simplify the expression, we omit embedding of diffusion timestep, trajectory timestep and rewards in and 19 In the implementation, the embedding of diffusion timestep and trajectory timestep are added to every input of CCA, SSA and TSA, and the embedding of rewards is added to every input of SSA and TSA.
Equation 16 17 T8
Output layer. We MLP layer the output layer convert the output of the temporal encoder layers into the noise we desire to predict.
C
Datasets
C.1 Detials of Datasets
We apply five real-world traffic flow datasets in three cities of different sizes including Hangzhou and Jinam:
(1) Hangzhou datasets: the road network contains 16 (4x4) intersections with two traffic flow datasets, including Hangzhou, and Hangzhou,- (2) Jinan datasets: the road network contains 12 (3x4) intersections with three traflic flow datasets, including Jinan Jinana and Hangzhou,. All these datasets are accessible
conto---ooialooooooo.... github.io/
We train AttendLiggt [T0], Efficient-Colighh (48) and Advanced-CoLight 13] in isolation for each dataset from scratch until convergence. Then we collect all transitions in the replay buffer for cach dataset during training. We present the converged performance of three methods in Table 4
Table Converged performance of methods used to collect offline datasets.
Methods
Hangzhou,
Hangzhou,
Jinan
Jinan
Jinan;
AttendLight
285.37
354.74
286.77
263.31
248.69
Efficient-CoLight
282.92
326.73
259.04
240.51
237.73
Advanced-CoLight
271.73
311.12
247.32
233.53
229.45
C.2
Missing Pattern
In TSC with missing data, missing patterns have significant impact on the performance of control. In this paper, shown in Figure conduct experiments random missing and kriging missing: (1) Random missing: traffic data collected by
for rewards and observations in every intersection randomly masked with 10%~550% probability. (2) Kriging missing: there always no traffic data collected in certain intersections with 6.25%v~25.00% 25.00% (1-intersection- -nteetioooo---iiteeeeettiion probability in Hangzhou, and Hangzhou,, -33%%~25500% (1- irrraattion--iinntrseeet probability in Jinanı, Jinany and Jinang, and all neighboring intersections surround missing intersections observable.
(a) Random missing
(b) Kriging missing
Figure Illustration of random missing and kriging missing pattern. Each node represents an intersection in the road network and blocks with masks are traffic data with missing value.
15

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D Baseline Methods
In this section, make brief introduction baseline approaches and the Store-and-forward method (SFM).
Baseline approaches. We adopt six baseline approaches in experiments as follows:
BC is a type imitation learning, where the agent learns to mimic the behavior of an expert demonstration. The agent is trained on a dataset of statc-action pairs from the expert, and the goal is to learn policy that can replicate the expert's 's actions given the same states.
CQL is RL algorithm that aims to learn conservative Q-function, which provides lower bound the true Q-values. This helps address issue of overestimation Q- vallles, which can lead poor performance practice.
TD3+BC combines the TD3 algorithm with behavioral cloning. By incorporating BC into TD3, the agent can leverage expert demonstrations to accelerate learning and improve sample efficiency. TD3+BC offers the benefits of both TD3's stability and BC's ability to learn from expert demonstra- tions.
DT is a sequence-to to totttt--ssuuueee sequence model that casts reinforcement learning as sequence modeling problem. It takes as input sequence of past states, actions, and rewards, and it outputs a sequence of future actions that maximize the expected cumulative reward. We build DT based on the code https://giitien
Diffuser a diffusion-based approach decision-making Diffuser focuses on generating sequences of actions that lead to desirable outcomes by iteratively refining these sequences. We build Diffuser based on the code https: http://gtttbbbbb com/ janerm/ dif fuser
DD is diffusion flffusion-bbsed approach for decision Docision-making, DD diffuses state trajectories and planning with inverse dynamics model. We build DD based on the code htttp:://gituu......... com/ anuraaajayydeciiiinn diffuser
To avoid non-convergence caused missing data, train baselines datasets without missing data and test them under data sata-missing scenarios with observations rewards imputed by SFM.
Store-and-forwaid method. Since baselines cannot handle the data-missing scenarios, adopt a rule- based SFM to impute observations and rewards for baselines. It is proved that SFM has stable performance compared to learning neural networks [14. In this paper. we model current observation as: f(V=1, k) Con I' (l,, k)) and f1(4, k) = &/2 Ei, L where VL_1 is intersection time t, l E Vt_, is a lanc and ly is the i's neighboring lane connected by traffic movements. We as 12 in this paper.
E Proof of Partial Rewards Conditioned Diffusion
To prove that the aim of partial rewards conditioned diffusion is same as goal in Equation assume that the observable part the trajectory and the missing part of the trajectory are collected by real sensors and virtual sensors separately, and the distribution of traffic data collected by two kinds of sensors are independent. Thus, the distribution in Equation 3 can be factorized as follows,
(() = p(e (Taka), (Tmis))
(Tama (B())) p(x (Tm))T))))(())
(20)
p(> (F v p(a" (T))
p(e (Traa)))((())))) (T)) p(e" p(ee (7mms)ly((m) (r))
The distribution without rewards condition p(2 (/)))/(())) can be regarded as marginal distribution of that with rewards condition (()((T))((T)) p(x (T) (T)),
p(x (T) p(r( p(r(T)) (()))))) (r)))
(21)
In this case, we can adopt the same diffusion model with classifier- free guidance to model (Tobe)7)))) y' (7)) and po (= (Tmis)l (7)).
16

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Additional Experiments Results
F.1 Performance without Missing Data
We train and test our method on all five datasets and compare our method with all basclines under no data-mise missing scenarios. DiffLight performs the best on over half of the datasets. Mcanwhile, DD demonstrates a better performance than Diffuser, which shows that diffusing only observations is better choice in TSC.
Table 5: Overall performance in scenarios without missing data.
Dataset
BC
CQL
TD3+BC
DT
Diffuser
DD
DiffLight
oz
342.26
318.42
327.19
297.46
289.64
284.79
283.92-+0.10
Dizz
374.9
353.04
364.8
338.33
357.34
328.63
319.79-25.13
Di
315.2
298.02
304.36
289.8
270.83
255.53
268.43.11.35
D
286.66
300.64
325.53
257.59
249.74
244.11
243.56=00033
DjN
296.05
288.42
281.59
247.71
241.44
241.34
1.3.
F.2 Influence of Unobserved Locations
In previous experiments, the unobserved intersections in kriging missing are not adjacent. In this section, we study the influence of unobserved locations. We provide another mask of Piz with missing rate of 25% in kriging missing, which contains missing intersection where all neighboring intersections are missing. The performance of this experiment shown Table DiffLight still demonstrates the best performance.
Table 6: Performance in different unobserved locations.
Dataset
BC
CQL
TD3+BC
DT
Diffuser
DD
DiffLight
Dz w/ neighbors
354.86
328.83
341.89
381.94
328.79
836.46
302.16+1.23
Duz w/o neighbors
398.77
361.11
447.79
427.62
465.61
745.85
344.02:88.72
F.3
Limit of Missing Rates
To further explore limits missing proportions, we conduct experiments the selected datasets in random missing with missing rates of 70% and 90%. In the experiment, DiffLight remains acceptable performance the missing rate 70%. When the missing rises 90%, the performance of DiffLight drops rapidly, which shows that the limit for the missing rate is around 70%.
Table 7: Limit of missing rates random missing.
Dataset
RM(70%)
RM(90%)
Diz 326.29
878.31
D
343.48
430.38
D 310.74
437.19
D
295.07
587.42
DI
289.01
668.41
F.4 Scalability of DiffLight
To further evaluate the efficacy and validate the performance of our approach, conduct experiments the New York dataset, which includes 48 intersections. the experiment on New York dataset, DiffLight achieves the best performance in most scenarios, demonstrating its ability to deal with complex traffic scenarios and control traffic signals in a lcrger-scale traffic network. In contrast, the performance of most baselines drops rapidly, due to the cumulative effect of emors state imputation and decision making
intersections.
17

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Table 8: Scalability of DiffLLigtt in random missing.
Dataset
Rate
BC
CQL
TD3+BC
DT
Diffuser
DD
DiffLight
10%
187.14
200.77
349.54
394.17
209.37
185.98
182.89
DNY
30%
226.23
254.73
540.18
605.81
241.32
229.44
244.93
50%
453.90
446.29
820.19
837.97
453.97
455.07
266.82
Table 9: Scalability of DiffLight in kriging missing.
Dataset
Rate
BC
CQL
TD3+BC
DT
Diffuser
DD
DifTLight
6.25%
515.40
242.15
496.41
894.76
741.99
765.64
197.22
DNY
12.50%
1304.52
470.69
859.98
930.78
951.49
1213.08
315.05
18.75%
1360.71
1154.71
989.99
1197.74
1034.02
929.25
350.66
25.00%
1442.31
1089.39
1108.67
1445.37
846.18
1393.23
454.56
F55
Additional Ablation Study on Diffusion Communication Mechanism
We further evaluate the effectiveness of DCM with DiffLight w/ DCM and DiffLLight w/o DCM. Table shows the comparison of these variants on Hangzhou, and Jinan, It should be noted that we adopt another mask of Diz used in Appendix F22 which contains a missing intersection where neighboring intersections are missing. Based on the results, we can find that DiffLighht w/ DCM shows better performance in kriging missing and the performance of DiffLight w/ DCM is close to the performance of DiffLight w/o DCM in random missing. It is proven that DCM sharing generated observations among intersections promote the performance of TSC with missing data effectively.
Table 10: Ablation study on Diffusion Communication Mechanism.
Dataset
Pattern and Rate
DiffLight w/ DCM
DiffLight w/o DCM
RM(50%)
304.71
303.13::2.23
D4z
KM(25%)
302.16:1..35
307.14
R.M(00%)
290. 190.02+1.226
289.16
KM(25%)
329.67
351.64+19.53
D4z
KM(25%) w/o neighbors
344.02-+8.72
351.64-+-..66
F66
Additional Ablation Study on the Inverse Dynamics
We further evaluate the effectiveness of the inverse dynamics (ID) with DiffLight w/ ID and DiffLight w/o ID. For DiffLight w/o inverse dynamics, remove the inverse dynamics and extend the dimension of the noise model generate both ohservations and actions. Table TT the comparison of these variants Hangzhou, Jinan Based on the results, we can find that DifiI right w/ inverse dynamics shows better performance in hoth random missing and kriging missing.
Table 11: Ablation study the inverse dynamics.
Dataset
Pattern and Rate
DiffLight w/ ID
DiffLight w/o ID
RM(50%) KM(25%)
303.91
572.61
Diz
301.08
386.92
RM(50%)
288.01
301.21
D
IN
KM(25%)
334.12
395.46
E.7 Time Cost
To effectively demonstrate the usability of DiffLLihht, conduct experiments to study the relationship between
inference speed and performance Table 12 and 13
We adopt models trained with 100 steps and test them
18

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different sampling steps. We can see that with the decrease in sampling steps, the performance of Difh remains stable. It proven that DiffLiggt is able handle the TSC task in acceptable time with good performance.
Table 12: Performance of DiffLLight on different sampling steps.
Dataset
Pattern and Rate
100-step
50-step
20-step
10-step
Diz
RM(55%)
301.62+0.42
301.90=2.79
300.75
300.95+1.77
D
Diz
KM(25%)
30..51+2.30
303.45=1.75
303.38=0007
306.77=2.70
DI
R.(550%)
288.51
289.45-:2.68
289.72:10.18
287.36 1.29
DIN
K.((2%%
0.99
337.17
33..31+12.66
325.20-16.37
Table 13: Inference time cost of DiffLLight on different sampling steps.
Dataset
Pattern and Rate
100-step
50-step
20-step
10-step
Diu DHZ. DIN
RM(50%) KM(25%)
150.36:114322
219.81
90.19-2.41
45.73:10.16
442.37:9.56
219.87=4.05
89.64=3.17
46.14+1.00
RM(50%)
44.191
218.31#2.69
45.50 90.23=1.77
DI
K.((5%)
8.8.
218.26+22.5
88.41=1.47
45.92-10.51
G Discussion on MissLight
To better clarify the core differences hetween Light and LissLiggt [1 we compare them from the following two aspects.
Model training. MissI Light is an online method with state imputation model and a reward imputation model, which means that interaction with the environment is necessary. In the online setting, if the method is trained in the physical environment, safety problems must be taken into consideration. If the method is trained in a simulated environment, the difference between physical environment and the simulated environment could affect the performance of the method to some extent when the online method is going to be employed in the physical environment. In contrast, our approach, DiffLight, is offline method based on the diffusion model. In the offiine setting, our method is trained using the collected dataset without interaction with the environment, which avoids the problems mentioned above.
Model composition. MissLight is two-stage method. In the first stage, state imputation and reward imputation models are used fill the missing data. In the second stage, the DQN algorithm is employed to complete the training process based on the imputed data. This approach suffers from the problem of error accumulation during the training process. However, our proposed DiffLight model, which incorporates both diffusion model and an inverse dynamics model, can simultancously train missing data and collaboratively achieve traffic signal control with missing data.
To better compare with MissLight, implement the SDQN-SDON (model-based) in 14 and replace the DQN algorithm with the CQL algorithm to adapt offline setting. replaced the DQN algorithm with different algorithuss in the offline setting and imputed the states with the SFM model. Note that all the baselines in Section were implemented with reference the EDQN-SDQP (transferred) method in MissLight. To distinguish the baseline of CQL implemented in Section 4.2 the baseline is named CQL (model-based). We provide the performance of CQL (model-based) in Table and Table
were
Table 14: Performance CQL (model-based) random missing.
Dataset
Rate
CQL
CQL (model-based)
DiffLight
10%
363.50
376.85
285.96
D1z
30%
368.53
381.92
293.10
50%
383.67
388.51
303.91
10%
299.07
303.46
273.17
D
30%
310.80
324.15
280.32
50%
322.25
361.40
288.01
19

---

Table 15: Performance of CQL
(model-based) kriging missing.
Dataset
Rate
CQL
CQL (model-based)
DiffLight
6.25%
317.69
389.66
291.80
12.50%
317.94
397.13
297.18
DHz
18.75%
319.18
449.80
299.96
25.00%
328.83
463.25
301.08
8.33%
302.35
374.20
280.83
Dj
16.67%
343.16
347.88
295.53
25.00%
398.66
400.55
334.12
DiftLight achieves competitive performance compared with CQL (transferred) and CQL (model-based)) The possible reason why DiffLight has better performance CQL (model-based) suffers from error accumulation caused by the reward imputation model while DiffLight can directly make decisions with Partial Rewards Conditioned Diffusion (PRCD).
20

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Reviews:
[{"review_id": "hqLbQNpbT4", "reviewer": "Reviewer_qAN4", "summary": "This paper focuses on traffic signal control under the condition of missing data, presenting DiffLight, a conditional diffusion model that integrates traffic data imputation and decision-making tasks. It introduces a partial rewards conditioned diffusion method to handle missing rewards (PRCD), employs a spatial-temporal transformer for noise modeling to capture intersection dependencies (STFormer), and proposes a diffusion communication mechanism for coordinated intersection control (DCM). Experiments demonstrate the effectiveness of DiffLight over various baselines. Further, the three components of DiffLight are studied and shown to be individually effective.", "questions": "**Minor comments**:\n\nLine 50 \"In addition, traffic data imputation for TSC with missing data is necessary.\" - somewhat repetitive\n\nLine 121 \"Diffuer\"\n\nLine 196 \"in both current intersection\" - in both \"the\" current intersection\n\nSection 3.2 might be revised for clarity.\n\nConsider including a requirements or setup file declaring the dependency versions used for the experiments in the paper. I had no issue reproducing some of the results, however dependencies may change substantially in the future.", "limitations": "Any potential negative societal impacts have been addressed.", "rating": 7, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "The paper is overall well written and presented clearly. A rigorous study of the suggested method is performed experimentally, confirming the contribution of each part of the DiffLight framework. Furthermore experiments showing the method can generalize well between differing levels of missing data are useful as this is likely the case in a real-world scenario.\n\nThis work may be relevant to the broader RL community as it uniquely handles missing data in diffusion based RL.", "weaknesses": "[W1] A direct discussion or comparison to [14] would be appropriate as it addresses a substantially similar problem. While it is primarily an online method, it does have an offline stage drawing the work closer to the proposed method. However, by comparing the presented results in this paper and [14] it seems unlikely [14] would perform better.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the reviewer recognizing the importance of our work and thank you for the detailed comments. Please find the point-by-point responses to the reviewer's comments below.\n\n> [W1] Discussion on MissLight\n\nThank you for highlighting the importance of a direct discussion between DiffLight and MissLight [1]. We apologize for our unclear expression and appreciate the opportunity to have a further discussion. We have made a brief discussion in the part of the Introduction in lines 40-44. To better clarify the core differences between our approach and MissLight, we compare them from the following two aspects:\n\n1. **Model training:** MissLight is an online method with a state imputation model and a reward imputation model, which means that interaction with the environment is necessary. In the online setting, if the method is trained in the physical environment, safety problems must be taken into consideration. If the method is trained in a simulated environment, the difference between the physical environment and the simulated environment could affect the performance of the method to some extent when the online method is going to be employed in the physical environment. In contrast, our approach, DiffLight, is an offline method based on the diffusion model. In the offline setting, our method is trained using the collected dataset without interaction with the environment, which avoids the problems mentioned above.\n2. **Model composition:** MissLight is a two-stage method. In the first stage, state imputation and reward imputation models are used to fill in the missing data. In the second stage, the DQN algorithm is employed to complete the training process based on the imputed data. This approach suffers from the problem of error accumulation during the training process. However, our proposed DiffLight model, which incorporates both a diffusion model and an inverse dynamics model, can simultaneously train on missing data and collaboratively achieve traffic signal control with missing data.\n\nAdditionally, it should be noted that MissLight as an online method can't be compared with DiffLight directly. To better compare with MissLight, we implement the SDQN-SDQN (model-based) in MissLight and replace the DQN algorithm with the CQL algorithm in order to adapt the offline setting. Note that all the baselines were implemented with reference to the SDQN-SDQN (transferred) method in MissLight. We replaced the DQN algorithm with different algorithms in the offline setting and imputed the states with the SFM model. To distinguish the baseline of CQL implemented in Section 4.2, the new baseline is named CQL (model-based) while CQL in Section 4.2 is named CQL (transferred).\n\n**Random Missing:**\n\n|Dataset|Rate|CQL (transferred)|CQL (model-based)|DiffLight|\n|-|-|-|-|-|\n|$\\mathcal{D}_{\\text{HZ}}^1$|10.00%|363.50|376.85|285.96|\n||30.00%|368.53|381.92|293.10|\n||50.00%|383.67|388.51|303.91|\n|$\\mathcal{D}_{\\text{JN}}^1$|10.00%|299.07|303.46|273.17|\n||30.00%|310.80|324.15|280.32|\n||50.00%|322.25|361.40|288.01|\n\n**Kriging Missing:**\n\n|Dataset|Rate|CQL (transferred)|CQL (model-based)|DiffLight|\n|-|-|-|-|-|\n|$\\mathcal{D}_{\\text{HZ}}^1$|6.25%|317.69|389.66|291.80|\n||12.50%|317.94|397.13|297.18|\n||18.75%|319.18|449.80|299.96|\n||25.00%|328.83|463.25|301.08|\n|$\\mathcal{D}_{\\text{JN}}^1$|8.33%|302.35|374.20|280.83|\n||16.67%|343.16|347.88|295.53|\n||25.00%|398.66|400.55|334.12|\n\nDiffLight achieves competitive performance compared with CQL (transferred) and CQL (model-based). The possible reason why DiffLight has better performance is that CQL (model-based) suffers from error accumulation caused by the reward imputation model while DiffLight can directly make decisions with Partial Rewards Conditioned Diffusion (PRCD).\n\n>  [Q1] Word and grammatical errors\n\nThank you for your feedback. We will correct the word and grammatical errors you mentioned and check for other possible errors.\n\n> [Q2] Code reproducibility\n\nThank you for your suggestion. We update a requirement into our code in the anonymous link. To enhance the reproducibility, we will include a readme file in the code. We apologize for our oversight of the readability and reproducibility.\n\nReference:\n\n[1] Mei, Hao, et al. \"Reinforcement learning approaches for traffic signal control under missing data.\" Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence. 2023.", "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": "", "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": "W2X7OTXObO", "reviewer": "Reviewer_3ABW", "summary": "The paper proposes a conditional diffusion framework to address the traffic signal control (TSC) problem under conditions of missing data. Utilizing Partial Rewards Conditioned Diffusion (PRCD) with classifier-free guidance, for both data imputation and decision making. The authors employ the DDIM sampling method and a spatial-temporal transformer noise predictor model to reconstruct the observation trajectory. The conditioning information is derived from partially observable rewards. A Diffusion Communication Mechanism (DCM) is introduced to exchange observation information between neighboring intersections. Finally, an inverse dynamic model is used to generate actions. Extensive experiments are conducted on datasets from multiple cities, with different missing patterns. The performance of the proposed approach is compared against multiple baseline methods.", "questions": "What boundary conditions ensure the effectiveness of this method? \nApart from assumptions such as missing data being independent of existing data, are there constraints such as limits on missing proportions and conflicts with neighboring traffic?", "limitations": "The authors discussed the limitations of the work in the Appendix. It is suggested that they put this part in the main body of the paper.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. Traffic signal control is a significant practical issue, and data missing is common in real-world applications. Solving this problem has substantial practical implications.\n\n2. The use of diffusion models to unify data imputation and 10 decision-making tasks in TSC is novel.", "weaknesses": "1. The selected datasets typically have few intersections and lack large-scale (e.g. thousands of intersections) datasets to validate scalability and cooperative performance.\n\n2. The comparison benchmarks and metrics are limited, lacking some methods, such as RL-based methods and GNN-based methods. Additionally, there is a lack of comparison for certain metrics, such as queue length and throughput.\n\n3. This paper contains many notations, formulas, and conclusions that are directly quoted without specific contextual explanations, making it confusing when reading for the first look.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their thoughtful and insightful comments. We respond to each of the points as follows:\n\n> [W1] Selection for datasets\n\nThank you for your comment. We appreciate the opportunity to elaborate on this. We would like to point out that DiffLight is designed to address the traffic signal control problem under data-missing scenarios, instead of focusing on scalability. Meanwhile, the selected datasets are commonly used in most of the literature [1, 2, 3, 4, 5, 6]. Besides, due to the limitation of computing resources and time, it is difficult to conduct experiments on large-scale datasets with thousands of intersections.\n\nHowever, there is no denying that scalability and cooperative performance play an essential role in applications. To further validate the scalability and cooperative performance of our approach, we conduct experiments on a larger dataset **New York**, which includes 48 intersections.\n\n**Random Missing:**\n\n|Dataset|Rate|BC|CQL|TD3+BC|DT|Diffuser|DD|DiffLight|\n|-|-|-|-|-|-|-|-|-|\n|$\\mathcal{D}_{\\text{NY}}$|10%|187.14|200.77|349.54|394.17|209.37|185.98|182.89|\n||30%|226.23|254.73|540.18|605.81|241.32|229.44|244.93|\n||50%|453.90|446.29|820.19|837.97|453.97|455.07|266.82|\n\n**Kriging Missing:**\n\n|Dataset|Rate|BC|CQL|TD3+BC|DT|Diffuser|DD|DiffLight|\n|-|-|-|-|-|-|-|-|-|\n|$\\mathcal{D}_{\\text{NY}}$|6.25%|515.40|242.15|496.41|894.76|741.99|765.64|197.22|\n||12.50%|1304.52|470.69|859.98|930.78|951.49|1213.08|315.05|\n||18.75%|1360.71|1154.71|989.99|1197.74|1034.02|929.25|350.66|\n||25.00%|1442.31|1089.39|1108.67|1445.37|846.18|1393.23|454.56|\n\nIn the new experiment on the New York dataset, DiffLight achieves the best performance in most of scenarios, demonstrating its ability to deal with complex traffic scenarios and control traffic signals in a larger scale traffic network. In contrast, the performance of most baselines drops rapidly, due to the cumulative effect of errors in state imputation and decision-making at more intersections.\n\n> [W2] Benchmarks and metrics\n\nThank you for pointing out the lack of benchmarks and metrics. We apologize for our oversight and appreciate the opportunity to make a further explanation. \n\n1. **Concerning comparison benchmarks**, we have included RL-based methods in experiments, including CQL and TD3+BC. To our knowledge, there is no GNN-based method proposed for the traffic singal control problem in the offline setting. Therefore, we choose CoLight [3], a GAT-based method widely used in the TSC task, as an additional baseline, to replace the DQN algorithm with the CQL algorithm, and conduct experiments on Hangzhou$_1$ and Jinan$_1$. However, due to the gap between offline RL and online RL, CoLight in the offline setting does not converge stably.\n2. **Concerning metrics**, average travel time, queue length and throughput do reflect the performance of methods in different aspects. Whereas average travel time is widely used in most of the literature [1, 2, 3, 4, 6] and is a more important metric for improving traffic efficiency. We apologize for our oversight and we will take queue length and throughput into consideration in future work in order to evaluate method performance more comprehensively.\n\n> [W3] Lack of explanations for notations, formulas and conclusions\n\nThank you for your feedback. We will revisit our paper carefully and incorporate specific contextual explanations for these notations, formulas and conclusions.\n\n> [Q1] Boundary conditions of the method\n\nThank you for highlighting the boundary conditions of the method. These are indeed important for the application of our approach and I'm pleased to make the following discussion:\n\n1. **Limits on missing proportions:** To further explore limits on missing proportions, we conduct experiments on the selected datasets in random missing with missing rates of 70% and 90%.\n\n|Dataset|Rate|DiffLight|\n|-|-|-|\n|$\\mathcal{D}_{\\text{HZ}}^1$|70.00%|326.29|\n||90.00%|878.31|\n|$\\mathcal{D}_{\\text{HZ}}^2$|70.00%|343.48|\n||90.00%|430.38|\n|$\\mathcal{D}_{\\text{JN}}^1$|70.00%|310.74|\n||90.00%|437.19|\n|$\\mathcal{D}_{\\text{JN}}^2$|70.00%|295.07|\n||90.00%|587.42|\n|$\\mathcal{D}_{\\text{JN}}^3$|70.00%|289.01|\n||90.00%|668.41|\n\nIn the new experiment, DiffLight remains acceptable performance at the missing rate of 70%. When the missing rate rises to 90%, the performance of DiffLight drops rapidly, which shows that the limit for the missing rate is around 70%.\n\n2. **Conflicts with neighboring traffic:** In the traffic network, all agents in the intersections make decisions at the same time with observations of the current intersection and neighboring intersections as input. Thus, there is no conflict in the order of decision-making. However, under data-missing scenarios, especially when the current intersection and neighboring intersections are all unobservable, agents' input could be unavailable, leading to conflict which could reduce the performance of the method. We design Diffusion Communication Mechanism (DCM) to alleviate this problem and conduct experiments in **Appendix G.3**.\n\nReference:\n\n[1] Mei, Hao, et al. \"Reinforcement learning approaches for traffic signal control under missing data.\" IJCAI. 2023.\n\n[2] Ye, Yutong, et al. \"InitLight: initial model generation for traffic signal control using adversarial inverse reinforcement learning.\" IJCAI. 2023.\n\n[3] Wei, Hua, et al. \"Colight: Learning network-level cooperation for traffic signal control.\" CIKM. 2019.\n\n[4] Zang, Xinshi, et al. \"Metalight: Value-based meta-reinforcement learning for traffic signal control.\" AAAI. 2020.\n\n[5] Yu, Zhengxu, et al. \"MaCAR: Urban traffic light control via active multi-agent communication and action rectification.\" IJCAI. 2021.\n\n[6] Zhang, Liang, et al. \"Expression might be enough: representing pressure and demand for reinforcement learning based traffic signal control.\" ICML. PMLR, 2022.", "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": "", "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": "lbrOIfIeXF", "reviewer": "Reviewer_PkZo", "summary": "The paper introduces \"DiffLight,\" a novel approach combining traffic data imputation and decision-making for Traffic Signal Control (TSC) under scenarios with missing data using a diffusion model framework. It employs partial rewards conditioned diffusion and a spatial-temporal transformer architecture to address challenges associated with incomplete data. The proposed model is tested extensively on existing datasets, demonstrating its efficacy in handling different missing data scenarios.", "questions": "1. Can you explain why MissLight is neglected? If you have offline data, it is easy to employ an offline version of MissLight as well.\n2. Why not compare on the existing dataset used in MissLight?", "limitations": "The paper discussed limitations.", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. Originality: The approach of using a conditional diffusion model to simultaneously perform traffic data imputation and decision-making in TSC is straightforward. The integration of partial rewards conditioned diffusion is particularly novel and helps mitigate the impact of data padding issues. \n\n2. Clarity: The paper is clearly written, with a logical structure that carefully explains the methodology and experimental setup, making it accessible and understandable.", "weaknesses": "1. There is a significant gap in the comparative analysis. The paper does not benchmark against relevant state-of-the-art methods like \"MissLight\" and other baseline diffusion models which are crucial for establishing the efficacy of the proposed approach.\n2. In MissLight, they used $D_{HZ}$, and $D_{NY}$ but this paper used new dataset, which is not clear why.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We highly appreciate your high-quality and valuable suggestions. We provide the point-by-point response as follows:\n\n> [W1 & Q1] Comparative analysis\n\nThank you for emphasizing the gap in the comparative analysis. We apologize for our unclear expression. Actually, all the baselines were implemented with reference to the SDQN-SDQN (transferred) method in MissLight [1]. We replaced the DQN algorithm with different algorithms in the offline setting and imputed the states with the SFM model.\n\nTo further evaluate the efficacy of the proposed approach, we employ an offline version of SDQN-SDQN (model-based) in MissLight and conduct experiments on Hangzhou$_1$ and Jinan$_1$. To distinguish the baseline of CQL in Section 4.2, it is named CQL (model-based) while CQL in Section 4.2 is named CQL (transferred).\n\n**Random Missing:**\n\n|Dataset|Rate|CQL (transferred)|CQL (model-based)|DiffLight|\n|-|-|-|-|-|\n|$\\mathcal{D}_{\\text{HZ}}^1$|10.00%|363.50|376.85|285.96|\n||30.00%|368.53|381.92|293.10|\n||50.00%|383.67|388.51|303.91|\n|$\\mathcal{D}_{\\text{JN}}^1$|10.00%|299.07|303.46|273.17|\n||30.00%|310.80|324.15|280.32|\n||50.00%|322.25|361.40|288.01|\n\n**Kriging Missing:**\n\n|Dataset|Rate|CQL (transferred)|CQL (model-based)|DiffLight|\n|-|-|-|-|-|\n|$\\mathcal{D}_{\\text{HZ}}^1$|6.25%|317.69|389.66|291.80|\n||12.50%|317.94|397.13|297.18|\n||18.75%|319.18|449.80|299.96|\n||25.00%|328.83|463.25|301.08|\n|$\\mathcal{D}_{\\text{JN}}^1$|8.33%|302.35|374.20|280.83|\n||16.67%|343.16|347.88|295.53|\n||25.00%|398.66|400.55|334.12|\n\nIn the new experiment, DiffLight achieves competitive performance compared with CQL (transferred) and CQL (model-based). The possible reason why DiffLight has better performance is that CQL (model-based) suffers from error accumulation caused by the reward imputation model while DiffLight can directly make decisions with Partial Rewards Conditioned Diffusion (PRCD).\n\nBesides, Diffuser [2] and Decision Diffuser [3] are the most representative work in the field of diffusion model for RL, which are included as baselines in much literature [9, 10, 11]. Thus, we choose them as our baselines rather than other diffusion-based methods.\n\n> [W2&Q2] Additional datasets\n\nThank you for highlighting the discussion on the selection of datasets. Actually, Hangzhou, Jinan and New York datasets are all commonly used in recent literature [1, 4, 5, 6, 7, 8]. We conducted extensive experiments on Hangzhou and Jinan datasets with different data-missing scenarios. To further evaluate the efficacy and validate the performance of our approach, we conduct experiments on the **New York** dataset, which includes 48 intersections.\n\n**Random Missing:**\n\n|Dataset|Rate|BC|CQL|TD3+BC|DT|Diffuser|DD|DiffLight|\n|-|-|-|-|-|-|-|-|-|\n|$\\mathcal{D}_{\\text{NY}}$|10%|187.14|200.77|349.54|394.17|209.37|185.98|182.89|\n||30%|226.23|254.73|540.18|605.81|241.32|229.44|244.93|\n||50%|453.90|446.29|820.19|837.97|453.97|455.07|266.82|\n\n**Kriging Missing:**\n\n|Dataset|Rate|BC|CQL|TD3+BC|DT|Diffuser|DD|DiffLight|\n|-|-|-|-|-|-|-|-|-|\n|$\\mathcal{D}_{\\text{NY}}$|6.25%|515.40|242.15|496.41|894.76|741.99|765.64|197.22|\n||12.50%|1304.52|470.69|859.98|930.78|951.49|1213.08|315.05|\n||18.75%|1360.71|1154.71|989.99|1197.74|1034.02|929.25|350.66|\n||25.00%|1442.31|1089.39|1108.67|1445.37|846.18|1393.23|454.56|\n\nIn the new experiment on the New York dataset, DiffLight achieves the best performance in most of scenarios, demonstrating its ability to deal with complex traffic scenarios and control traffic signals in a larger scale traffic network. In contrast, the performance of most baselines drops rapidly, due to the cumulative effect of errors in state imputation and decision-making at more intersections.\n\nReference:\n\n[1] Mei, Hao, et al. \"Reinforcement learning approaches for traffic signal control under missing data.\" Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence. 2023.\n\n[2] Janner, Michael, et al. \"Planning with Diffusion for Flexible Behavior Synthesis.\" *International Conference on Machine Learning*. PMLR, 2022.\n\n[3] Ajay, Anurag, et al. \"Is Conditional Generative Modeling all you need for Decision Making?.\" *The Eleventh International Conference on Learning Representations*.\n\n[4] Ye, Yutong, et al. \"InitLight: initial model generation for traffic signal control using adversarial inverse reinforcement learning.\" Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence. 2023.\n\n[5] Wei, Hua, et al. \"Colight: Learning network-level cooperation for traffic signal control.\" Proceedings of the 28th ACM international conference on information and knowledge management. 2019.\n\n[6] Zang, Xinshi, et al. \"Metalight: Value-based meta-reinforcement learning for traffic signal control.\" Proceedings of the AAAI conference on artificial intelligence. Vol. 34. No. 01. 2020.\n\n[7] Yu, Zhengxu, et al. \"MaCAR: Urban traffic light control via active multi-agent communication and action rectification.\" Proceedings of the Twenty-Ninth International Conference on International Joint Conferences on Artificial Intelligence. 2021.\n\n[8] Zhang, Liang, et al. \"Expression might be enough: representing pressure and demand for reinforcement learning based traffic signal control.\" International Conference on Machine Learning. PMLR, 2022.\n\n[9] Li, Wenhao, et al. \"Hierarchical diffusion for offline decision making.\" *International Conference on Machine Learning*. PMLR, 2023.\n\n[10] Venkatraman, Siddarth, et al. \"Reasoning with Latent Diffusion in Offline Reinforcement Learning.\" *The Twelfth International Conference on Learning Representations*.\n\n[11] Zhu, Zhengbang, et al. \"Madiff: Offline multi-agent learning with diffusion models.\" *arXiv preprint arXiv:2305.17330* (2023).", "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": "", "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": "WBj9VZGPUI", "reviewer": "Reviewer_V6Ax", "summary": "This paper proposes a conditional diffusion model named DiffLight, which is able to unify traffic data imputation and decision-making for TSC when data is incomplete. Specifically, it proposes a partial reward conditional diffusion method to avoid the negative effects brought by the padded values of missing data. Additionally, a novel spatial-temporal transformer architecture and a diffusion communication mechanism are designed to capture spatiotemporal dependencies between intersections as well as enhance cooperative control among them. Extensive experiments on five datasets demonstrate the effectiveness of the DiffLight. Besides, the source code provided in this paper is accessible and available for use.", "questions": "Could you provide a specific example to explain the design of the DCM mechanism?", "limitations": "See weaknesses.", "rating": 7, "confidence": 5, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "S1: This paper studies a significant problem of traffic signal control with missing data, which is often overlooked by researchers but is prevalent in real urban traffic scenarios. So, the solutions proposed in this paper will benefit practical use about TSC a lot. Besides, the paper is well-written and easy to follow.\nS2: The idea of unifying the problems of traffic data imputation and traffic signal control decision-making in a model is interesting, also wise and reasonable, but has never been studied before. The design of partial reward conditional diffusion (PRCD) with classifier-free guidance is novel, which makes it feasible to model the complex distribution of traffic data, especially in scenarios with missing traffic data. Additionally, the paper provides theoretical proof of PRCD's feasibility to demonstrate how PRCD avoids the negative impacts of padding.\nS3: In the noise model of DiffLight, the paper designs the spatial-temporal transformer architecture (STFormer) to model the spatiotemporal dependencies between multiple intersections in traffic signal control. Furthermore, the paper introduces a diffusion communication mechanism, which assists in capturing the spatiotemporal dependencies between multiple intersections by disseminating the observational information generated by the STFormer during the backward process. This mechanism enables effective traffic signal control in difficult scenarios, such as simultaneous data loss at the current intersection and neighboring intersections.", "weaknesses": "W1: The authors should further explain how the Diffusion Communication Mechanism (DCM) enables information communication among multiple intersections when data is missing at both the current intersection and neighboring intersections. This part is not clear enough.\nW2: This paper only considers traffic signal control under two typical types of missing data patterns. While it is undeniable that random missing and Kriging missing are the most common patterns in real life, future research could explore traffic signal control under a wider variety of missing data patterns, including mixed missing data scenarios.\nW3: There are some symbols in the paper that are not correctly defined. For example:\n- At line 146, \\(\\tau\\) is defined as the observation trajectory, but at line 152, it states \\(\\tau_{i}\\) represents the neighboring intersection. I think here \\(\\tau_{i}\\) should denote the observation trajectory of the neighboring intersection.\n- In the experimental section, at lines 220 and 221, the evaluation metric (Average Travel Time, ATT) is defined. Is there a more objective formula definition and explanation for it?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We are delighted that the reviewer found our motivation interesting and reasonable. Thank you for your positive and insightful comments. We respond to each of the points below:\n\n> [W1 & Q1] Explanation of Diffusion Communication Mechanism\n\nThank you for your comments. We have made a brief introduction in **Section 3.2**. We apologize for our unclear expression and appreciate the opportunity to clarify this. Diffusion Communication Mechanism (DCM) is designed to enhance information communication among multiple intersections. In DCM, the states of neighboring intersection $x^k(\\tau^i)$ diffused by diffusion model at diffusion step $k$ would be used to calculate $x^0(\\tau^i)$ and then  $x^0(\\tau^i)$ would be sent to its current intersections. The agent in the current intersection would take $x^0(\\tau^i)$ as the condition to generate the states of the current intersection $x^{k-1}(\\tau)$ at diffusion step $k-1$.\n\n> [W2] Missing patterns of data\n\nThank you for highlighting the complex missing patterns of data in the real world. Undoubtedly, the missing patterns of data in the real world are far more complex than the random and Kriging missing patterns mentioned. We completely agree with this. In future work, we will follow your suggestion to further explore traffic signal control methods under mixed data-missing scenarios.\n\n> [W3] Symbols and metrics\n\nThank you for your detailed inspection of the symbol definitions. We will carefully correct these incorrect symbol definitions to improve the paper. Additionally, regarding the explanation of average travel time (ATT), it is the most commonly used metric in the field of traffic signal control. This metric represents the average travel time of all vehicles from entering the road network to leaving the intersection, and it effectively reflects the performance of traffic signal control. The calculation formula is as follows:\n\n$$\n\\text{ATT}=\\frac{1}{N} \\sum_{i=1}^{N} \\left ( t_{i}^{l}-t_{i}^{e} \\right ),\n$$\n\nwhere $N$ is the total number of vehicles entering the road network, $t_{i}^{e}$ and $t_{i}^{l}$ are the entering time and leaving time for the $i$-th vehicle respectively.", "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": "", "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: This paper tackles the practical application of traffic signal control under missing data, proposes a novel diffusion-based model architecture, and performs a sound evaluation that shows the proposed approach outperforms various relevant baselines and provides insights through ablation. Presentation is generally clear (though some typos and grammar errors must be fixed for the camera ready version). Moreover, as pointed by reviewers, the approach can be useful for other applications, making it relevant to the broader RL community.

The new experimental results (comparison with MissLight, results on larger-scale NY dataset, boundary conditions on missing rates...) and explanations (e.g., why kriging is more challenging) provided during the rebuttal period make the paper clearer and sounder and should be included in the camera ready version.
Decision: Accept (spotlight)