Research map / Multi-agent systems and games / Human-AI and goal-conditioned
Learning Verified Safe Neural Network Controllers for Multi-Agent Path Finding
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Proposes VSMANC, jointly training decentralized control barrier functions (DCBFs) and neural controllers for multi-agent path finding with a unified loss, plus formal verification (Marabou) guided retraining using counterexamples.
Problem
Learning-based controllers for multi-agent path finding (MAPF) are safety-critical, but data-driven control barrier functions carry no guarantee of correctness, so the safety of learned controllers cannot be theoretically assured.
Approach
Jointly trains neural DCBFs and neural controllers from agent-environment interaction with a unified loss (worst-case safe loss, classical control reference loss, goal distance loss), then distills the DCBF into an MLP and verifies it with Marabou, retraining on the counterexamples produced by the verifier.
Key results
- VSMANC reports a safety rate of 0.99 with 32 drones in the ablation (random map), versus 0.90 for the variant without formal verification-guided retraining.
- Relative to the second-best method, VSMANC improves safety rate by 3% to 37% and reduces time steps by 16% to 30%.
- In the outdoor simulation with 10 drones over 20 trials, VSMANC had no collisions (proportion 1.00), while the best baseline MDBC reached 0.90.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add worst-case safe loss LW S (ablation) | VSMANC · Random, cross, and street maps (32 agents) | safety rate: 0.89 -> 0.99; 0.87 -> 0.99; 0.88 -> 0.99 | Helped |
| Add classical control loss Lref (ablation) | VSMANC · Random, cross, and street maps (32 agents) | running time step: 101 -> 75; 113 -> 87; 98 -> 74 | Helped |
| Add goal distance loss Lgoal (ablation) | VSMANC · Random, cross, and street maps (32 agents) | running time step: 119 -> 75; 124 -> 87; 117 -> 74 | Helped |
| Add formal verification-guided retraining (ablation) | VSMANC · Random, cross, and street maps (32 agents) | safety rate: 0.90 -> 0.99; 0.90 -> 0.99; 0.91 -> 0.99 | Helped |
| Use formal verification-generated counterexamples instead of random-sampling counterexamples (ablation) | DCBF retraining · Table 2 evaluation | safety rate: 0.994 vs 0.956 | Helped |
| Vary counterexample label C and retraining rounds (ablation) | DCBF retraining · Table 2 evaluation | safety rate: 0.954 -> 0.998; 0.947 -> 0.968 | Helped |
| Vary student network architecture for DCBF distillation (ablation) | DCBF student network · Distillation evaluation | F1 score: 0.22; 0.69; 0.31 | Mixed |
| Use VSMANC rather than the strongest competing method | MAPF methods · Outdoor simulation (20 trials) | proportion of safe trajectories: 0.90 -> 1.00 | Helped |
Surprising findings
- Formal verification-guided retraining alone, without the worst-case safe loss, still maintains a fairly high safety rate (0.90 vs 0.99 for the full method).
Limitations
- Supervised learning framework requires standard control policies and heuristic path-finding guidance.
- Distillation for verification may lose rigor and weaken controller safety guarantees.
- UAV simulations use basic double-integrator dynamics.
Experimental setup
Datasets: simulated UAV shape formation environment (200 patterns)
Benchmarks: UAV shape formation (random, cross, street maps) outdoor DJI UAV simulation
Metrics: safety rate running time steps proportion of collision-free episodes
Baselines: MDBC S2M2 MADDPG-safe ALF CS-MARL
Builds on: Decentralized Control Barrier Function (MDBC) Marabou knowledge distillation MADDPG
Closest papers by meaning
- Verified Safe Reinforcement Learning for Neural Network Dynamic Models (NeurIPS 2024 · similarity 0.87)
- Learn to Follow: Decentralized Lifelong Multi-Agent Pathfinding via Planning and Learning (AAAI 2024 · similarity 0.87)
- HMARL-CBF – Hierarchical Multi-Agent Reinforcement Learning with Control Barrier Functions for Safety-Critical Autonomous Systems (NeurIPS 2025 · similarity 0.85)
- MAPF-GPT: Imitation Learning for Multi-Agent Pathfinding at Scale (AAAI 2025 · similarity 0.85)
- A Physics-Informed Machine Learning Framework for Safe and Optimal Control of Autonomous Systems (ICML 2025 · similarity 0.85)
- Discrete GCBF Proximal Policy Optimization for Multi-agent Safe Optimal Control (ICLR 2025 · similarity 0.85)
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