2025/05/20 by Sharifi, Sina, Erfan Yazdandoost Hamedani, Hamedani, Erfan Yazdandoost +2
Decision Sciences · Engineering · #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Reservoir Engineering and Simulation Methods #Risk and Portfolio Optimization #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2505.14647
openalex publication_date 2025/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Bilevel optimization involves a hierarchical structure where one problem is nested within another, leading to complex interdependencies between levels. We propose a single-loop, tuning-free algorithm that guarantees anytime feasibility, i.e., approximate satisfaction of the lower-level optimality condition, while ensuring descent of the upper-level objective. At each iteration, a convex quadratically-constrained quadratic program (QCQP) with a closed-form solution yields the search direction, followed by a backtracking line search inspired by control barrier functions to ensure safe, uniformly positive step sizes. The resulting method is scalable, requires no hyperparameter tuning, and converges under mild local regularity assumptions. We establish an O(1/k) ergodic convergence rate in terms of a first-order stationary metric and demonstrate the algorithm's effectiveness on representative bilevel tasks.