Collaborative Research: Computationally Efficient Algorithms for Large-scale Bilevel Optimization Problems

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The recent advancements in machine learning and power systems with hierarchical decision-making structure necessitate developing efficient schemes to solve bilevel optimization problems. A bilevel optimization problem is a hierarchical decision-making process and an important class of mathematical models in which finding the optimal decision (the upper-level problem) depends on anticipating another decision-making problem (the lower-level problem). Despite the progress in studying bilevel optimization, most existing methods could be slow or inefficient when applied in large-scale, uncertain, or distributed settings. This project aims to address these challenges by examining novel reformulations of bilevel optimization and developing computationally efficient algorithms for solving hierarchical decision-making problems. The outcomes of this project will be transformational for energy storage systems, investment and operation planning in power systems, recommendation platforms, and speech and image recognition software. On the education front, this project will provide a stimulating and innovative research environment to include under-representative and minority students in the project research; it will also incorporate the development of curricular material for courses in the PIs’ institutions. This project lays out a detailed agenda for exploring bilevel optimization reformulations and developing efficient and scalable schemes to address major limitations of state-of-the-art bilevel optimization frameworks when confronted with the challenges of recently emerged paradigms in machine learning and power systems. The research encompasses three different thrusts: (I) Examining reformulations of nonconvex bilevel optimization and offering new insights on how to reformulate a bilevel optimization problem with the goal of finding a local optimum. (II) Developing computationally efficient methods with fast convergence guarantees for bilevel optimization problems under uncertainty by leveraging tools from stochastic optimization and online learning. (III) Investigating bilevel optimization problems in a decentralized regime with the goal of developing and analyzing distributed algorithms with local computations and communications.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.