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This research introduces Flow-Matched Motion Priors (FMP), an online reward mechanism for imitation learning in robotics that utilizes flow matching and optimal transport to improve policy generalization. The method addresses limitations of adversarial objectives by training neural potentials along paths connecting current rollouts to expert motion banks, resulting in more stable locomotion on physical robots like the Unitree G1. By reducing falls and accelerating offline fitting time compared to baseline approaches, this work advances the practical deployment of reinforcement learning agents in dynamic environments.
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Flow-Matched Motion Priors: Online Optimal-Transport Rewards for Imitation Learning

arXiv3 min read

arXiv:2609.15631v1 Announce Type: new Abstract: Learning a motion prior requires a reward that guides a policy from its current behavior toward demonstrated motion. Adversarial Motion Priors (AMP) provide such a reward with a discriminator. However, adversarial objectives can become uninformative when policy and expert supports are far apart. A naive use of optimal transport (OT) averages matched expert successors into a barycentric target. Averaging across gait phases can weaken the target's joint motion. We introduce Flow-Matched Motion Priors (FMP), an online scalar reward learned from paths connecting current rollout histories to an expert motion bank. Entropic OT supplies the coupling. Before each policy update, we train a neural potential with flow matching (FM) along the rollout-to-expert paths, endpoint-gradient supervision, and relative-value calibration. The actor receives only physical observations and the reward remains a scalar, as in AMP. Controlled reward-model experiments show substantially better generalization beyond the fitting rollout than value-only or endpoint-only fitting. On Unitree G1, matched 50-million-transition experiments compare FMP with AMP, a barycentric OT reward, and nested ablations under demonstration and fixed-pose initialization. FMP produces stable forward walking at 0.727 m/s from demonstration resets and 0.338 m/s from a fixed default pose. In the fixed-pose condition, it incurs 129 falls versus 243 for the endpoint-only control. Against a static score-gradient teacher, dynamic FM reduces score-increment error at interpolation fractions 0.25 and 0.50 while using 29% less offline fitting time.

Abstract:Learning a motion prior requires a reward that guides a policy from its current behavior toward demonstrated motion. Adversarial Motion Priors (AMP) provide such a reward with a discriminator. However, adversarial objectives can become uninformative when policy and expert supports are far apart. A naive use of optimal transport (OT) averages matched expert successors into a barycentric target. Averaging across gait phases can weaken the target's joint motion. We introduce Flow-Matched Motion Priors (FMP), an online scalar reward learned from paths connecting current rollout histories to an expert motion bank. Entropic OT supplies the coupling. Before each policy update, we train a neural potential with flow matching (FM) along the rollout-to-expert paths, endpoint-gradient supervision, and relative-value calibration. The actor receives only physical observations and the reward remains a scalar, as in AMP. Controlled reward-model experiments show substantially better generalization beyond the fitting rollout than value-only or endpoint-only fitting. On Unitree G1, matched 50-million-transition experiments compare FMP with AMP, a barycentric OT reward, and nested ablations under demonstration and fixed-pose initialization. FMP produces stable forward walking at 0.727 m/s from demonstration resets and 0.338 m/s from a fixed default pose. In the fixed-pose condition, it incurs 129 falls versus 243 for the endpoint-only control. Against a static score-gradient teacher, dynamic FM reduces score-increment error at interpolation fractions 0.25 and 0.50 while using 29% less offline fitting time.

Robotics (cs.RO)

arXiv:2609.15631 [cs.RO]

(or arXiv:2609.15631v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2609.15631 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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