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This paper introduces the Featurized Occupation Measure (FOM), a finite-dimensional primal-dual interface for occupation-measure formulations in numerical optimal control, bridging the gap between global HJB methods and scalable trajectory optimization. FOM enables both explicit weak-form schemes and implicit simulator-based sampling methods, using approximate HJB subsolutions as numerical certificates to guide primal search. The authors prove asymptotic consistency and demonstrate that FOM preserves certified lower bounds with blockwise error control, even under time shifts and model perturbations, making global certificates reusable for certificate-guided optimization.
Unlock globally optimal control policies in high-dimensional systems by unifying trajectory optimization with Hamilton-Jacobi-Bellman methods via a novel "Featurized Occupation Measure" framework.
Numerical optimal control is commonly divided between globally structured but dimensionally intractable Hamilton-Jacobi-Bellman (HJB) methods and scalable but local trajectory optimization. We introduce the Featurized Occupation Measure (FOM), a finite-dimensional primal-dual interface for the occupation-measure formulation that unifies trajectory search and global HJB-type certification. FOM is broad yet numerically tractable, covering both explicit weak-form schemes and implicit simulator- or rollout-based sampling methods. Within this framework, approximate HJB subsolutions serve as intrinsic numerical certificates to directly evaluate and guide the primal search. We prove asymptotic consistency with the exact infinite-dimensional occupation-measure problem, and show that for block-organized feasible certificates, finite-dimensional approximation preserves certified lower bounds with blockwise error and complexity control. We also establish persistence of these lower bounds under time shifts and bounded model perturbations. Consequently, these structural properties render global certificates into flexible, reusable computational objects, establishing a systematic basis for certificate-guided optimization in nonlinear control.
