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

Simulation-trained manipulation policies can exploit privileged state information to learn effective contact-rich behaviours, but deployment requires acting from partial observations such as noisy camera images. A common solution is teacher-student distillation, in which a visuomotor policy is trained to reproduce the actions of the privileged expert. This requires the student to jointly infer the task-relevant state and relearn the expert's action mapping that is already available. An alternative is to reuse the state-based expert and learn only a perceptual interface that reconstructs its missing state inputs. However, minimising the state estimate error alone does not necessarily minimise the downstream control error induced by these estimates. To bridge this gap, we train a visual state estimator using both direct state supervision and an action-consistency loss backpropagated through the frozen, differentiable expert. A scheduled objective first establishes a physically meaningful state estimate and progressively emphasises errors that affect the expert's actions. Across five goal-conditioned manipulation tasks, retaining the expert consistently outperforms direct pixel-to-action imitation from the same expert demonstration corpus. We further demonstrate sim-to-real transfer on a physical Panda robot, achieving 76% success without retraining the underlying expert.

Small observation or action errors can compound during closed-loop execution and disrupt a trained imitation learning policy. We study whether the original expert demonstrations can improve robustness through test-time hidden-state steering without additional demonstrations or policy retraining. Our analysis of a trained policy finds that expert hidden-state variation is concentrated in relatively few dimensions, while the directions capturing this variation differ across regions. Motivated by this geometry, we propose Diffeomorphic Hidden-State Steering (DHS), which learns an invertible nonlinear coordinate map from expert hidden states obtained by replaying the demonstrations through the frozen policy. DHS attenuates coordinates with low expert variance more strongly than those with high variance, then maps the modified coordinates back to hidden-state space. This allows steering directions to vary with the current hidden state while retaining every coordinate. Across four simulated manipulation tasks, DHS improves mean success under observation noise over the unmodified Transformer policies. Controlled comparisons yield higher mean success with learned nonlinear coordinates than with linear coordinates under both hard projection and full-rank rescaling. Combining DHS with action smoothing improves mean success rate under observation noise in certain tasks compared with action smoothing alone.

Constructing action targets from measured robot motion is an established approach in imitation learning. Under interaction constraints, however, command-state discrepancy may reflect control demands that motion alone does not capture. We investigate when this information matters and how to exploit it. Across three real-robot tasks, task and phase analyses reveal larger supervision gaps under constrained interaction, while selective command retention provides evidence of locally useful command information. Building on these findings, we propose Command-State Discrepancy Weighting (CSDW), which accounts for robot response times and combines subsequent progress, persistent unmet demand, and demand changes into continuous weights for command supervision. The method requires no task-phase annotations or changes to policy architecture or inference. CSDW improves over uniform command supervision on constrained tasks, while methods perform similarly in the less constrained task. Project page: https://seen-e.github.io/CSDW/.