On Finding Small Hyper-Gradients in Bilevel Optimization: Hardness Results and Improved Analysis

Bilevel optimization reveals the inner structure of otherwise oblique optimization problems, such as hyperparameter tuning, neural architecture search, and meta-learning. A common goal in bilevel optimization is to minimize a hyper-objective that implicitly depends on the solution set of the lower-level function. Although this hyper-objective approach is widely used, its theoretical properties have not been thoroughly investigated in cases where \textit{the lower-level functions lack strong convexity}. In this work, we first provide hardness results to show that the goal of …

analysis architecture cs.ai cs.lg function hyperparameter math.oc meta meta-learning neural architecture search optimization search set small solution