On the Stability and Generalization of First-order Bilevel Minimax Optimization

• URL: http://arxiv.org/abs/2604.20115v1
• Date: Wed, 22 Apr 2026 02:27:24 GMT
• Title: On the Stability and Generalization of First-order Bilevel Minimax Optimization
• Abstract summary: We provide the first systematic generalization analysis for first-order gradient-based bilevel minimax solvers with lower-level minimax problems.<n>Our results reveal a precise trade-off among stability, generalization gaps, and practical settings.
• Score: 4.009802081742405
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bilevel optimization and bilevel minimax optimization have recently emerged as unifying frameworks for a range of machine-learning tasks, including hyperparameter optimization and reinforcement learning. The existing literature focuses on empirical efficiency and convergence guarantees, leaving a critical theoretical gap in understanding how well these algorithms generalize. To bridge this gap, we provide the first systematic generalization analysis for first-order gradient-based bilevel minimax solvers with lower-level minimax problems. Specifically, by leveraging algorithmic stability arguments, we derive fine-grained generalization bounds for three representative algorithms, including single-timescale stochastic gradient descent-ascent, and two variants of two-timescale stochastic gradient descent-ascent. Our results reveal a precise trade-off among algorithmic stability, generalization gaps, and practical settings. Furthermore, extensive empirical evaluations corroborate our theoretical insights on realistic optimization tasks with bilevel minimax structures.

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