GAMBIT is an opening chess move in which a player sacrifices a piece, typically a pawn, to gain a positional advantage later in the game. Analogously, in multi-robot coordination, individual robots may need to forgo locally reward-maximising behaviours to improve overall team performance. Such self-sacrificial behaviours are difficult to capture with manually designed heuristics, particularly in dense, interaction-rich environments. Focusing on double-integrator continuous dynamics, this work studies how to learn such coordinated heuristics over motion primitives for multi-robot trajectory execution. Our framework, GAMBIT, first learns coordinated motion-primitive selection through imitation learning and subsequently fine-tunes the policy through reinforcement learning. We further introduce a safeguarded rollout mechanism with backup trajectories that guarantees collision-free execution at all times. Experiments demonstrate that GAMBIT substantially outperforms a range of baselines, including centralised motion planners and decentralised reactive planners, while exhibiting strong scalability. In particular, it coordinates over a thousand robots with planning latency below a few hundred milliseconds in continuous domains.

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