Safety-Critical Contextual Control via Online Riemannian Optimization with World Models
Summary: arXiv:2604.19639v1 Announce Type: cross
Abstract
Modern world models are becoming too complex to admit explicit dynamical descriptions. We study safety-critical contextual control, where a Planner must optimize a task objective using only feasibility samples from a black-box Simulator, conditioned on a context signal ξt. We develop a sample-based Penalized Predictive Control (PPC) framework grounded in online Riemannian optimization, in which the Simulator compresses the feasibility manifold into a score-based density p̂(u | ξt) that endows the action space with a Riemannian geometry guiding the Planner’s gradient descent. The barrier curvature κ(ξt), the minimum curvature of the conditional log-density -ln p̂(·|ξt), governs both convergence rate and safety margin, replacing the Lipschitz constant of the unknown dynamics.
Main Findings
Our main result is a contextual safety bound showing that the distance from the true feasibility manifold is controlled by the score estimation error and a ratio that depends on κ(ξt), both of which improve with richer context.
Key Highlights
- Development of a sample-based Penalized Predictive Control (PPC) framework.
- Introduction of online Riemannian optimization to enhance control strategies.
- Demonstration of how barrier curvature impacts convergence rate and safety margins.
- Establishment of a contextual safety bound that leverages score estimation error.
- Simulation results confirming the advantages of contextual PPC over traditional models.
Simulation Results
Simulations on a dynamic navigation task confirm that contextual PPC substantially outperforms marginal and frozen density models. Notably, the advantage of contextual PPC grows after environmental shifts, indicating its robustness and adaptability in changing conditions.
Conclusion
This work presents a significant advancement in safety-critical contextual control by utilizing a novel approach centered on online Riemannian optimization. The findings suggest that as world models continue to evolve in complexity, the integration of contextual information and optimization techniques will be essential for ensuring safety and efficiency in AI systems.
Future Directions
Future research could investigate the application of this framework in various domains such as robotics, autonomous vehicles, and other safety-critical systems. Additionally, exploring the implications of different types of context signals and their impact on the optimization process could further enhance the robustness of the proposed methods.