Scaling to Large Teams

Our multi-agent diffusion planner holds roughly 90% success through $N=32$ and leads the MILP baseline by double digits through $N=64$, from $+15.6$ to $+33.3$ points. At $N=128$ the two methods tie on success (34.4 against 33.3) and our safety falls to 41.9%. We therefore present $N\le64$ as the result and $N=128$ as the point where the current model runs out.

Setting: Dubins Car environment, mixed heterogeneous specification, where each agent samples one component (sequence, branch, cover, loop, or signal) per episode, on a fixed goal grid at goal scale 2.0. Rates are means over 3 episodes.

Read the safe rate together with the finish rate. The MILP baseline's higher safety at $N=128$ (64.1 against our 41.9) is not a win. Its finish rate there is 66.1, so it is partly safe because fewer of its agents ever complete their tours. Safety on its own rewards an agent that does very little.

$N=128$ is a tie. The $+1.0$ success gap sits inside the noise of 3 episodes on a single seed, whereas the gaps at $N\le64$ (from $+15.6$ to $+33.3$) are far outside it.

Setup and step budget. The arena grows with the goal scale, from side 6 at scale 1.0 to 10 at scale 2.0 and 14 at scale 3.0, and the step budget was raised at the larger scales (7200 at scale 2.5, 9000 at scale 3.0). At goal scale 2.0, the configuration reported above, the budget stays at its default of 4800, which is the tightest budget-to-distance ratio in the sweep. It was measured rather than assumed: at $N=64$ only 2.6% of agents run out of steps and 93.8% reach their final waypoint, so the horizon is not what limits these numbers. Temporal operators are interpreted over plan steps, which advance on reach rather than on wall-clock, so a slow agent is not penalized by the specification.

Scaling the goal set apart trades one failure for another. It buys safety, by giving agents somewhere to go that is not through each other. Beyond goal scale 1.5 it starts costing plan quality, because the planner was never trained on goals that far apart. The two tables below are the same runs, and past that point they move in opposite directions.

$N=8$ separates the two causes. With 8 agents there is no crowding to relieve: the safe rate is 100.0 at every goal scale it was run at. Spreading the goals cannot help those agents and cannot hurt them through traffic, yet their finish rate still falls from 100.0 at goal scale 1.5 to 83.3 at 2.5. The only variable left is how far apart the goals are, so that drop is the planner on its own, out of distribution on a goal set wider than the one it was trained on.

It is goal spread, not arena size. Goal scales 1.5 and 2.0 run in the same arena of side 10, and the $N=8$ finish rate still falls from 100.0 to 91.7 between them. What the model has not seen is the distance between goals, not the dimensions of the map.

It is not the step budget. Ranked by budget per unit of goal distance, the scales run 1.5, then 3.0, then 2.5, then 2.0. If the horizon were the limit, scale 3.0 would finish better than scale 2.0 at $N=8$. It finishes worse, 87.5 against 91.7, so that ordering rules the budget out.

Where this leaves scaling: at $N=32$ goal scaling is not needed, with safety at roughly 95% or better at every scale from 1.5 up. At $N=64$ it is needed, since unscaled goals leave safety near 58% and goal scale 2.0 is the first setting to clear 80%. At $N=128$ it stops helping, with safety saturating near 43% from goal scale 2.5 onward, and because more spread also costs plan quality, no setting rescues $N=128$. The remaining gap points at the planner rather than the tracking controller (GCBF+ reports high safety on single-goal reach in an arena of side 16, larger than any used here), so reaching that regime calls for training or tuning the planner on the wider goal set rather than spreading the goals further.