Using a small-gain argument from control theory, the authors prove the standard single-loop bilevel optimization algorithm converges linearly in the strongly convex setting.
Exponential convergence bounds using integral quadratic constraints
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Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem
Using a small-gain argument from control theory, the authors prove the standard single-loop bilevel optimization algorithm converges linearly in the strongly convex setting.