# Reference-Conditioned Inverse Dynamics

The work proposes ActFirst-OPD, which decouples environment interaction from full-response generation: the student infers and executes actions through reference-conditioned inverse dynamics using its current interaction context and a reference next observation, switches to autonomous next-action prediction once the transition deviates from the reference trajectory, and asynchronously generates full think-then-act responses from the collected interaction contexts for token-level teacher supervision; across 0.6B, 1.7B and 4B Qwen3 students it achieves average wall-clock training speedups of 2.3x on ALFWorld, 1.8x on WebShop and 4.9x on ScienceWorld over Vanilla OPD, while matching or exceeding mean task success rate in eight of nine benchmark-model settings.

The work proposes ActFirst-OPD, which decouples environment interaction from full-response generation: the student infers and executes actions through reference-conditioned inverse dynamics using its current interaction context and a reference next observation, switches to autonomous next-action prediction once the transition deviates from the reference trajectory, and asynchronously generates full think-then-act responses from the collected interaction contexts for token-level teacher supervision; across 0.6B, 1.7B and 4B Qwen3 students it achieves average wall-clock training speedups of 2.3x on ALFWorld, 1.8x on WebShop and 4.9x on ScienceWorld over Vanilla OPD, while matching or exceeding mean task success rate in eight of nine benchmark-model settings.