Designing capable neural policies for multi-agent pathfinding (MAPF), which map local observations to action distributions, represents an important challenge in multi-agent learning, with practical relevance to scalable collective automation problems such as warehouse logistics. In contrast to prior studies focusing primarily on individual policy design, this study explores a meta-level Mixture-of-Experts (MoE) approach to learning-based MAPF. Specifically, given a collection of compact yet high-performing experts specialised for different map distributions, our architecture learns a router that selectively fuses their outputs according to each agent's local situation. We instantiate and validate this MoE approach with a commonly used graph neural network-based policy as well as a newly developed recursive action-token refinement model. Combined with supervised and reinforcement learning fine-tuning of the experts, our experiments show that MoE generally improves upon the pretrained policy and outperforms existing leading methods. At the same time, our findings reveal that appropriately trained, parameter-matched monolithic models still outperform MoE, highlighting a nuanced role for map-distribution MoE for MAPF.
Figures & tables
Figure 1: MoE framework. A learned router fuses map-distribution experts taking each agent’s local observation.
Figure 2: ReCAT architecture. Following the spatial encoding (left), an action token is refined through message passing from other tokens of agent i and matching action tokens of neighbouring agents (right). Tensor shapes use H=W=2Robs+1 , C feature channels, token dimension d , and action embedding dimension da .
Figure 3: Main results. Top : success rates (%) for MAGAT (left) and ReCAT (right); values in parentheses indicate percentage-point differences from the base pretrained policy, the Avg column denotes the unweighted mean across the six map distributions, and the Uniform row combines expert logits with equal weights. Bottom : performance across seven map distributions and varying numbers of agents, comparing base pretrained policies, MoE policies, larger monolithic policies with SFT+RL, HMAGAT, and MAPF-GPT-DDG. Shaded bands indicate 95% bootstrap confidence intervals for SoC.
CS-PIBT
w/o CS-PIBT
Model
SR (%)
Rel. SoC
Time ( s )
SR (%)
Rel. SoC
Time ( s )
MAGAT (485K)
78.4
1.752
0.879
62.4
2.161
0.501
MAGAT Uniform
82.6
1.578
1.073
67.6
2.017
0.778
MAGAT MoE
83.4
1.555
1.173
67.8
1.984
0.821
MAGAT (2.1M, SFT+RL)
87.3
1.470
0.733
73.6
1.829
0.412
ReCAT (121K)
81.4
1.664
0.921
69.5
1.981
0.535
Table 1: Aggregated scores with and without CS-PIBT over the same 2,800 instances across six map distributions. SR denotes success rate; relative SoC and runtime are means over all instances, including failures.
Expert
Maze
WH.
Room
Random
Sort.
Stripes
Empty
Avg.
MAGAT-MoE
Maze
97.4
11.0
12.4
10.1
63.3
94.5
65.5
50.6
WH.
0.3
78.9
0.5
1.1
0.7
0.0
12.1
13.4
Room
1.0
1.7
83.3
2.5
18.4
5.4
0.6
16.1
Random
1.2
8.4
3.9
86.3
17.5
0.1
21.8
19.9
ReCAT-MoE
Maze
70.4
22.0
28.2
25.0
49.7
69.5
42.4
43.9
WH.
8.7
72.6
8.1
6.5
9.0
9.1
18.9
19.0
Table 2: Mean expert mixture weights (%). Columns correspond to evaluation distributions.
Warehouse
Maze
Training
SR (%) ↑
Rel. SoC ↓
SR (%) ↑
Rel. SoC ↓
MAGAT (485K)
Pretrain
78.8
1.900
70.8
1.826
SFT
85.6
1.646
74.4
1.711
RL (w/o PL)
83.8
1.928
75.0
1.854
RL (PL)
87.2
1.792
77.4
1.707
SFT+RL (w/o PL)
90.0
1.649
80.4
1.708
Table 3: Expert performance on Warehouse and Maze across different training strategies. PL denotes the Plackett–Luce likelihood of the candidate sequence examined by PIBT; w/o PL uses only the selected action’s probability for RL updates.
MAGAT-MoE (2.1M)
MAGAT (2.1M)
ReCAT-MoE (676K)
ReCAT (782K)
MAPF-GPT-DDG (2M)
# Agents
ms/step
Goal (%)
SoC
ms/step
Goal (%)
SoC
ms/step
Goal (%)
SoC
ms/step
Goal (%)
SoC
ms/step
Goal (%)
SoC
1,000
5.9 ( 79.9 )
100
1.017
1.8 (81.8)
100
1.015
11.4 (83.5)
100
1.019
6.3 (85.7)
100
1.013
40.0 (115.3)
100
1.032
10,000
13.1 (727.7)
100
1.095
5.0 ( 707.1 )
100
1.090
97.7 (809.9)
100
1.080
60.3 (771.1)
100
1.079
424.2 (1145.2)
100
1.100
100,000
620.6 (7402.2)
97.122
2.318
285.6 ( 7068.5 )
98.335
2.233
2189.8 (9022.2)
99.466
2.104
1227.5 (8191.5)
99.711
2.020
4476.2 (11435.6)
96.555
2.415
Table 4: Scalability assessment. Times report network inference. The versions with CS-PIBT is shown with parentheses (in Python unlike [ 2 , 3 ] using C++). Goal denotes the percentage of agents at their goals. SoC is normalised by ∑i∈Adist(si,gi) .
Table 5: Performance across different MoE training strategies w.r.t. success-rate gains over the pretrained ReCAT (121K), in percentage points. Icons: frozen or updated parameters.
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 4: Examples from the four in-distribution map generators. Each column shows four different layouts; black cells denote obstacles and white cells are traversable.
Model
Parameters
MAGAT (485K)
484,933
MAGAT (2.1M)
2,154,181
ReCAT (121K)
121,299
ReCAT (782K)
781,843
MLP router (190K)
190,980
MAGAT-MoE (2.1M)
2,130,712
Appendix
Table 6: Parameter counts of the evaluated MAGAT and ReCAT configurations, including all expert parameters in each mixture.
Figure 5: Success rate and mean relative SoC without CS-PIBT across seven map distributions. Each point averages 100 instances; SoC is reported relative to LaCAM3 with a 60s time limit. Shaded bands indicate 95% bootstrap confidence intervals for SoC.
Variant
Maze
WH.
Room
Random
Sort.
Stripes
Empty
Avg.
MAGAT-MoE
∖ Maze
75.0 (+0.2)
89.2 (-2.0)
88.2 (-1.4)
87.4 (+3.0)
99.0 (+0.0)
45.3 (-1.0)
100.0 (+0.0)
83.4 (-0.2)
∖ WH.
77.0 (+2.2)
87.6 (-3.6)
87.6 (-2.0)
87.2 (+2.8)
99.0 (+0.0)
43.7 (-2.7)
100.0 (+0.0)
83.2 (-0.5)
∖ Room
74.8 (+0.0)
89.4 (-1.8)
83.8 (-5.8)
87.0 (+2.6)
98.8 (-0.2)
43.7 (-2.7)
100.0 (+0.0)
82.5 (-1.1)
∖ Random
77.2 (+2.4)
89.8 (-1.4)
88.8 (-0.8)
84.4 (+0.0)
98.6 (-0.4)
46.7 (+0.3)
100.0 (+0.0)
83.6 (+0.0)
Full MoE
74.8
91.2
89.6
84.4
99.0
46.3
100.0
83.6
ReCAT-MoE
∖ Maze
85.4 (-1.6)
95.4 (-0.2)
96.4 (-1.0)
93.0 (+0.4)
100.0 (+0.2)
66.0 (-1.3)
100.0 (+0.0)
90.9 (-0.5)
Appendix
Table 7: Success rates (%) with CS-PIBT after excluding one expert while retaining router-training data from all four distributions. Parentheses give changes in percentage points relative to the full four-expert MoE.