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Stochastic Frank-Wolfe Algorithm for Constrained Bilevel Optimization With Improved Per-Iteration Complexity
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DOI：10.1109/TSP.2025.3596231.png)
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Abstract
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Bilevel optimization, where one optimization problem is inherently nested within another, has gained significant attention due to its extensive applications in machine learning, such as hyperparameter optimization and meta-learning. Most existing algorithms are designed to address unconstrained bilevel optimization problems, with few are capable of effectively tackling complex constrained settings. To address this gap, we propose a novel, fully single-loop stochastic Frank-Wolfe algorithm. This algorithm incorporates a Hessian-inverse-vector approximation technique, momentum-based gradient tracking, and a Frank-Wolfe update. Our proposed algorithm improves per-iteration complexity and achieves lower sample complexity compared to existing Frank-Wolfe algorithms for bilevel optimization. We also conduct numerical simulations to demonstrate the efficacy of our algorithm compared to state-of-the-art methods.
Keywords:
Stochastic Frank-Wolfe algorithm
bilevel optimization
hypergradient approximation
variance reduction technique
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13.7
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