Safety-Critical Contextual Control via Online Riemannian Optimization with World Models

• URL: http://arxiv.org/abs/2604.19639v1
• Date: Tue, 21 Apr 2026 16:28:36 GMT
• Title: Safety-Critical Contextual Control via Online Riemannian Optimization with World Models
• Abstract summary: We study safety-critical contextual control, where a Planner must optimize a task objective using only feasibility samples from a black-box Simulator.<n>We develop a sample-based Penalized Predictive Control framework grounded in online Riemannian optimization.<n>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 $(_t)$, both of which improve with richer context.
• Score: 7.720387326648637
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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 $ξ_t$. 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 $\hat{p}(u \mid ξ_t)$ that endows the action space with a Riemannian geometry guiding the Planner's gradient descent. The barrier curvature $κ(ξ_t)$, the minimum curvature of the conditional log-density $-\ln\hat{p}(\cdot\midξ_t)$, governs both convergence rate and safety margin, replacing the Lipschitz constant of the unknown dynamics. 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 $κ(ξ_t)$, both of which improve with richer context. Simulations on a dynamic navigation task confirm that contextual PPC substantially outperforms marginal and frozen density models, with the advantage growing after environment shifts.

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