Collaborative Research: Efficient Bilevel Optimization Methods for Planning and Control

Bilevel optimization is a foundational tool for modeling hierarchical decision-making problems, becoming increasingly prevalent in various fields including machine learning, transportation, energy systems, and robotics. However, existing research on bilevel optimization often focuses on simplified or unconstrained settings, limiting its applicability to practical scenarios that require safe, real-time decision-making under complex constraints. This project aims to bridge this gap by developing efficient and scalable algorithms for constrained, nonconvex bilevel problems, with particular emphasis on planning and control tasks in safety-critical domains. The outcomes of this research will provide general-purpose optimization tools that benefit a broad range of applications in robotics, learning, and autonomous systems. Software developed through this project will be released as open-source packages, enabling broad adoption across academia and industry. Furthermore, this project includes a comprehensive educational and outreach component to engage students at multiple academic levels, foster hands-on learning experiences, and broaden participation in STEM fields. This project advances the theory and practice of bilevel optimization by designing efficient, safe, and scalable algorithms tailored specifically to constrained, nonconvex bilevel problems in planning and control. The research comprises two main thrusts. In the first thrust, a novel control-theoretic framework will be developed to systematically design bilevel solvers. By modeling optimization algorithms as controlled dynamical systems, this approach will leverage techniques from control theory to establish algorithms with provable convergence guarantees and anytime safety. The foundational work in this thrust specifically targets scalability, non-unique lower-level solutions, and nonconvexities at both optimization levels. In the second thrust, this framework will be applied to two high-impact domains: (i) safe inverse optimal control and reinforcement learning, where the objective is to recover control policies from expert demonstrations under strict safety constraints; and (ii) safe interactive planning for navigation in crowded environments, integrating real-time decision-making with predictive models of human motion. By addressing fundamental challenges in hierarchical safety-critical decision-making, this research will advance the state of the art in optimization, control, and autonomous systems, benefiting both theoretical developments and practical applications. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.