2023/05/22 by Xiaoyu Wang, Wang, Xiaoyu, Rui Pan +4 · 2 citations
Computer Science · Engineering · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning and ELM #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2305.13153
openalex publication_date 2023/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Bilevel optimization has found successful applications in various machine learning problems, including hyper-parameter optimization, data cleaning, and meta-learning. However, its huge computational cost presents a significant challenge for its utilization in large-scale problems. This challenge arises due to the nested structure of the bilevel formulation, where each hyper-gradient computation necessitates a costly inner optimization procedure. To address this issue, we propose a reformulation of bilevel optimization as a minimax problem, effectively decoupling the outer-inner dependency. Under mild conditions, we show these two problems are equivalent. Furthermore, we introduce a multi-stage gradient descent and ascent (GDA) algorithm to solve the resulting minimax problem with convergence guarantees. Extensive experimental results demonstrate that our method outperforms state-of-the-art bilevel methods while significantly reducing the computational cost.