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Contractive Dynamical Imitation Policies for Efficient Out-of-Sample Recovery
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Proposes SCDS, a state-only contractive dynamical-system imitation policy built from contracting RENs plus bijective coupling layers, trained by unconstrained optimization with soft-DTW loss and given OOS loss upper bounds.
Problem
Imitation policies learned from demonstrations can behave unreliably in out-of-sample states; stable DS policies guarantee convergence but ignore transient behavior, while existing contractive methods rely on constrained optimization or need state derivatives.
Approach
Model the policy as a continuous-time contracting REN in a latent space, with a learnable linear projection and coupling-layer bijections as output map, so contractivity holds for any parameters and training uses only states with unconstrained gradient descent through differentiable ODE solutions.
Key results
- On OOS rollouts on LASA-2D, SCDS achieves MSE 0.32 vs 1.78 for the best baseline (SDS-EF), and soft-DTW 1.72 vs 6.91 (SNDS).
- On Robomimic-14D OOS, SCDS achieves MSE 2.68 vs 6.88 (SNDS), and the paper reports reducing the best baseline error by up to a factor of 2.5 averaged across four tasks.
- Robot deployment in Isaac Lab reports average OOS soft-DTW errors of 3.68 ± 0.33 (Franka Lift) and 1.94 ± 0.37 (Jackal navigation) over 50 initial states.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SCDS instead of the strongest listed baseline | LASA-2D OOS · LASA-2D | MSE: 1.78 ± 0.34 -> 0.32 ± 0.15 | Helped |
| Use SCDS instead of the strongest listed baseline | LASA-2D OOS · LASA-2D | soft-DTW: 6.91 ± 1.46 -> 1.72 ± 0.54 | Helped |
| Use SCDS instead of the strongest listed baseline | LASA-4D OOS · LASA-4D | MSE: 2.33 ± 0.47 -> 1.09 ± 0.21 | Helped |
| Use SCDS instead of the strongest listed baseline | LASA-4D OOS · LASA-4D | soft-DTW: 9.85 ± 0.63 -> 2.58 ± 0.30 | Helped |
| Use SCDS instead of the strongest listed baseline | Robomimic-6D OOS · Robomimic-6D | MSE: 1.15 ± 0.81 -> 0.89 ± 0.26 | Helped |
| Use SCDS instead of the strongest listed baseline | Robomimic-6D OOS · Robomimic-6D | soft-DTW: 2.67 ± 1.40 -> 1.71 ± 0.53 | Helped |
| Use SCDS instead of the strongest listed baseline | Robomimic-14D OOS · Robomimic-14D | MSE: 6.88 ± 2.16 -> 2.68 ± 0.65 | Helped |
| Use SCDS instead of the strongest listed baseline | Robomimic-14D OOS · Robomimic-14D | soft-DTW: 12.17 ± 2.70 -> 6.27 ± 0.48 | Helped |
| Use SCDS instead of the strongest listed baseline | Robomimic-6D in-sample · Robomimic-6D | MSE: 0.50 ± 0.28 -> 0.56 ± 0.22 | Hurt |
| Use SCDS instead of the strongest listed baseline | Robomimic-6D in-sample · Robomimic-6D | soft-DTW: 1.01 ± 0.66 -> 1.05 ± 0.37 | Hurt |
| Use SCDS instead of the strongest listed baseline | LASA-2D in-sample · LASA-2D | MSE: 0.02 ± 0.01 -> 0.02 ± 0.01 | No clear effect |
| Use SCDS instead of the strongest listed baseline | LASA-4D in-sample · LASA-4D | MSE: 0.03 ± 0.01 -> 0.03 ± 0.01 | No clear effect |
Surprising findings
- BC-style baselines diverge from the target on OOS initial states, as expected without stability guarantees, while stable baselines reach the target but deviate from expert data during transients.
Limitations
- Longer horizons for rapidly changing expert data increase computation, trading off cost against imitation accuracy.
- Experiments limited to simulated tasks with short horizons on LASA and Robomimic.
Experimental setup
Datasets: LASA Robomimic
Benchmarks: LASA Robomimic
Metrics: MSE soft-DTW
Baselines: SNDS SDS-EF BC NCDS C-GMR CDSP CVF
Builds on: recurrent equilibrium networks neural ODE soft-DTW Stable Neural Dynamical Systems Stable Dynamical Systems with Euclideanizing Flows
Closest papers by meaning
- Learning When to Stop: Selective Imitation Learning Under Arbitrary Dynamics Shift (NeurIPS 2026 · similarity 0.88)
- Neural Contractive Dynamical Systems (ICLR 2024 · similarity 0.87)
- Policy Decorator: Model-Agnostic Online Refinement for Large Policy Model (ICLR 2025 · similarity 0.87)
- Diverse Policies Recovering via Pointwise Mutual Information Weighted Imitation Learning (ICLR 2025 · similarity 0.87)
- Improving Generative Behavior Cloning via Self-Guidance and Adaptive Chunking (NeurIPS 2025 · similarity 0.87)
- Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning (NeurIPS 2024 · similarity 0.87)
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