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

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 xi_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 xi_t) that endows the action space with a Riemannian geometry guiding the Planner's gradient descent. The barrier curvature kappa(xi_t), the minimum curvature of the conditional log-density -lnhat{p}(dotmidxi_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 kappa(xi_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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Source: arXiv cs.AI | 2026-04-22