Finite-Sample Metric Non-Collapse for Geometrically Supervised Latent World Models in Control
We establish a finite-sample learning-to-control theory for geometrically supervised latent models of nonlinear deterministic systems. Geometric supervision is used only during training: simulator state, proprioception, or state estimates with independently validated metric and directional error bounds supply observable-state distances and tangent directions, while deployment remains observation- and action-conditioned. We introduce an encoder-only local--global metric hinge that enforces directional resolution and separated-state discrimination. Under regular observable-factor, coverage, finite-capacity approximation, and uniform $C^{1,1}$ hypotheses, a computable one-sided regularizatio...
| Authors | Alain Bensoussan, Minh-Nhat Phung, Minh-Binh Tran |
|---|---|
| Primary category | math.OC |
| Published | 7 August 2026 |
| Last updated at source | 23 August 2026 |
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