On the Condition Number Dependency in Bilevel Optimization
Researchers have established a new lower bound for bilevel optimization problems, specifically $\Omega(\kappa_y^{5/2} \epsilon^{-2})$. This finding reveals a gap in the condition number dependency between bilevel and minimax problems. The study also extends these lower bounds to various settings, including higher-order smooth functions, stochastic oracles, and convex objectives. AI
IMPACT Establishes theoretical limits for optimization algorithms, potentially influencing future AI model training techniques.