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arXiv · 2610.41540

FOCUS: First-Order Control Using Optimal Transport Supervision for Imitation from Observations

João A. Cândido Ramos·Lionel Blondé·Hugues Vinzant·Jacopo Castellini·Alexandros Kalousis
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Abstract

Imitation learning from observations must recover behavior from state-only demonstrations without known temporal correspondence. Differentiable simulators provide pathwise policy gradients, but differentiating through long, contact-rich trajectories can make optimization unstable. We introduce FOCUS, which combines local optimal-transport alignment with short-horizon differentiable actor-critic learning. FOCUS matches agent rollout windows to multiple sampled expert segments using a soft best-of-$K$ objective that emphasizes locally compatible matches. The resulting transport-based costs provide differentiable imitation rewards, while a learned critic bootstraps value beyond the rollout horizon. FOCUS requires neither temporally aligned trajectories nor expert-aligned initialization or teacher forcing. Across contact-rich locomotion tasks in DFlex, including a musculoskeletal humanoid controlled by 152 muscle activations, FOCUS improves sample efficiency and training stability over adversarial imitation-from-observation methods and prior differentiable imitation baselines.

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João A. Cândido Ramos, Lionel Blondé, Hugues Vinzant, Jacopo Castellini, Alexandros Kalousis. 2026-10-30. FOCUS: First-Order Control Using Optimal Transport Supervision for Imitation from Observations. https://arxiv.org/abs/2610.41540

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