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arXiv · 2305.13153

Effective Bilevel Optimization via Minimax Reformulation

Xiaoyu Wang·Rui Pan·Renjie Pi·Jipeng Zhang
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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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Xiaoyu Wang, Rui Pan, Renjie Pi, Jipeng Zhang. 2023-05-22. Effective Bilevel Optimization via Minimax Reformulation. https://arxiv.org/abs/2305.13153

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