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Nested Convex-Body Chasing for Online Optimization with Evolving Feasible Sets

arXiv · AI, language, vision and robotics · article · Aug 29, 2026 · UTC

We study online optimization with nested shrinking feasible regions in two settings: convex optimization with nested evolving feasible sets (CONES) and adversarial constrained online convex optimization (COCO). Our algorithms separate loss control from geometric movement: constrained minimizers and cumulative-loss tests preserve regret guarantees, while a deterministic resettable nested convex-body chaser limits movement. For CONES with a $G$-Lipschitz, $μ$-strongly convex objective on a diameter-$D$ domain, we chase intersections of the current feasible set with adaptive objective sublevel se

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