Effective Bilevel Optimization via Minimax Reformulation

• URL: http://arxiv.org/abs/2305.13153v4
• Date: Mon, 04 Nov 2024 02:09:11 GMT
• Title: Effective Bilevel Optimization via Minimax Reformulation
• Authors: Xiaoyu Wang, Rui Pan, Renjie Pi, Jipeng Zhang,
• Abstract summary: We propose a reformulation of bilevel optimization as a minimax problem. Under mild conditions, we show these two problems are equivalent. Our method outperforms state-of-the-art bilevel methods while significantly reducing the computational cost.
• Score: 23.5093932552053
• License:
• Abstract: 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.

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