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Online Relational Inference for Evolving Multi-agent Interacting Systems
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Proposes Online Relational Inference (ORI), which treats the adjacency matrix as a trainable parameter updated by online backpropagation with a relation-aware adaptive learning rate (AdaRelation) and a Trajectory Mirror augmentation, evaluated on evolving springs/charged simulations and CMU MoCap.
Problem
Identifying hidden interaction graphs in evolving multi-agent systems from streaming trajectories, where offline-trained NRI-style encoder-decoder models fail to adapt to changing interactions, parameters, or dynamics.
Approach
Replace the encoder with a directly trainable adjacency matrix updated by online gradient descent through a frozen-architecture trajectory decoder, and adapt its learning rate based on the recent change in the adjacency matrix (AdaRelation), plus axis-flip augmentation (Trajectory Mirror).
Key results
- On springs with evolving interaction, ORI with MPMa reaches 96.4% average relation accuracy vs 61.6% for MPM.
- On charged systems with evolving interaction, ORI with MPMr reaches 95.3% accuracy vs 51.7% for MPM, though NRI has lower MSE there.
- On CMU MoCap, ORI's MSE is generally higher than MPM's (e.g., mse 1: 1.31e-4 for ORI w/ MPMr vs 1.17e-4 for MPM).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace encoder-based inference with a trainable adjacency matrix in ORI | NRI and MPM decoders · Springs and charged systems with evolving interactions | relation accuracy (%): Springs: 61.6 -> 96.4; Charged: 51.7 -> 95.3 | Helped |
| Use AdaRelation rather than constant adjacency learning rates (ablation) | ORI with NRIr · Charged, evolving interaction | relation accuracy (%): 89.3 -> 90.9; 87.0 -> 90.9 | Helped |
| Use AdaRelation rather than constant adjacency learning rates (ablation) | ORI with MPMr · Charged, evolving interaction | relation accuracy (%): 92.2 -> 95.3; 94.1 -> 95.3 | Helped |
| Use AdaRelation rather than constant adjacency learning rates (ablation) | ORI with NRIr · Springs, evolving interaction | relation accuracy (%): 90.2 -> 94.2; 94.4 -> 94.2 | Mixed |
| Use AdaRelation rather than constant adjacency learning rates (ablation) | ORI with MPMr · Springs, evolving interaction | relation accuracy (%): 93.1 -> 95.2; 95.5 -> 95.2 | Mixed |
| Add Trajectory Mirror (ablation) | ORI with MPMr · Springs, evolving interaction | relation accuracy (%): 80.5 -> 95.2 | Helped |
| Add Trajectory Mirror (ablation) | ORI with MPMr · Charged, evolving interaction | relation accuracy (%): 90.2 -> 95.3 | Helped |
| Use AdaRelation rather than constant adjacency learning rates (ablation) | ORI with NRIr · Charged, evolving interaction and parameter | relation accuracy (%): 83.4 -> 84.8; 73.8 -> 84.8 | Helped |
| Use AdaRelation rather than constant adjacency learning rates (ablation) | ORI with MPMr · Charged, evolving interaction and parameter | relation accuracy (%): 92.5 -> 92.1; 88.8 -> 92.1 | Mixed |
| Use AdaRelation rather than constant adjacency learning rates (ablation) | ORI with NRIr · Springs, evolving interaction and parameter | relation accuracy (%): 94.9; 95.0; 94.7 | No clear effect |
| Remove Trajectory Mirror (ablation) | ORI with MPMr · Springs, evolving interaction and parameter | relation accuracy (%): 85.1 -> 95.0 | Hurt |
| Remove Trajectory Mirror (ablation) | ORI with MPMr · Charged, evolving interaction and parameter | relation accuracy (%): 79.6 -> 92.1 | Hurt |
Surprising findings
- In charged systems, ORI achieves much higher relation accuracy than baselines while baselines show lower trajectory MSE, suggesting MSE is not a reliable proxy for relation quality.
- Trajectory Mirror, rather than AdaRelation, accounts for most of the accuracy gain in the ablations.
Limitations
- Not evaluated on directed interaction graphs or variable numbers of agents.
- Charged-system and CMU MoCap MSE are not better than baselines; accuracy gains do not translate to lower trajectory error.
- Learning-rate and hyperparameters (eta_min, eta_max, initial rate up to 100k for MoCap) are dataset-specific.
Experimental setup
Datasets: synthetic springs simulations (NRI code) synthetic charged simulations (NRI code) CMU MoCap (processed with dNRI code)
Benchmarks: synthetic springs synthetic charged CMU MoCap
Metrics: relation accuracy MSE on predicted trajectory
Baselines: NRI MPM dNRI CoGNN-AR CoGNN-LSTM CoGNN-TC
Builds on: neural relational inference MPM dNRI online expert mixture
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