Geometric Distributional Control: Learning Progress with Partial Structural Knowledge

Abstract:Real-time control often sits between two limiting regimes. Predictive optimization and model-based control are powerful when dynamics, parameters, objectives, and online planning models are specified; reinforcement learning can relax this requirement, but must infer long-horizon value signals from sequential data and interaction, making training slow, high-variance, and hard to scale in large action spaces. This middle regime is common in systems including autonomous driving, warehouse robotics, traffic control, and delivery drones: partial geometry, physics, rules, or constraints are known, yet the local direction of task progress remains uncertain. Geometric Distributional Control (GDC) is designed for this partial-knowledge setting. It factorizes control into feasibility and progress: known geometry, rules, constraints, and response maps define an executable scaffold, while progress-weighted feasible data learns the missing directional signal on that scaffold. The learned score acts as a Bellman-like local value-gradient, selecting actions that make progress without requiring global Bellman recursion, a fully specified planner, or a black-box policy that absorbs both feasibility and preference. This knowledge can be lightweight and partial, such as simple dynamics, safety filters, local maps, constraint projectors, or lower-level response maps; it need not encode full dynamics or a long-horizon objective. Offline, GDC fits a progress-tilted distribution from short known-feasible snippets with weak signed progress certificates. Online, its score is projected through the scaffold and applied in receding-horizon feedback. We prove that this score descends a data-induced soft progress value and validate GDC on structured multilevel optimization and SUMO route-progress driving, where it improves over known-only solvers and learning baselines while preserving scaffold-enforced feasibility.

Robotics (cs.RO); Systems and Control (eess.SY)

arXiv:2609.06331 [cs.RO]

(or arXiv:2609.06331v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2609.06331 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.