  For many multiagent control problems, neural networks (NNs) have enabled
promising new capabilities. However, many of these systems lack formal
guarantees (e.g., collision avoidance, robustness), which prevents leveraging
these advances in safety-critical settings. While there is recent work on
formal verification of NN-controlled systems, most existing techniques cannot
handle scenarios with more than one agent. To address this research gap, this
paper presents a backward reachability-based approach for verifying the
collision avoidance properties of Multi-Agent Neural Feedback Loops (MA-NFLs).
Given the dynamics models and trained control policies of each agent, the
proposed algorithm computes relative backprojection sets by (simultaneously)
solving a series of Mixed Integer Linear Programs (MILPs) offline for each pair
of agents. We account for state measurement uncertainties, making it well
aligned with real-world scenarios. Using those results, the agents can quickly
check for collision avoidance online by solving low-dimensional Linear Programs
(LPs). We demonstrate the proposed algorithm can verify collision-free
properties of a MA-NFL with agents trained to imitate a collision avoidance
algorithm (Reciprocal Velocity Obstacles). We further demonstrate the
computational scalability of the approach on systems with up to 10 agents.
