BROS: Bias-Corrected Randomized Subspaces for Memory-Efficient Single-Loop Bilevel Optimization

Fuente: arXiv
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Main Authors: Zhang, Hengrui, Kong, Boao, Zhang, Engao, Yuan, Kun
Format: Preprint
Published: 2026
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author Zhang, Hengrui
Kong, Boao
Zhang, Engao
Yuan, Kun
author_facet Zhang, Hengrui
Kong, Boao
Zhang, Engao
Yuan, Kun
contents Stochastic bilevel optimization (SBO) has become a standard framework for hyperparameter learning, data reweighting, representation learning, and data-mixture optimization in deep learning. Existing exact single-loop SBO methods and memory-efficient surrogate SBO methods either create severe memory pressure for large lower-level neural networks or lack competitive convergence guarantees under standard assumptions. In this paper, we propose BROS, a memory-efficient single-loop SBO method with the same convergence rate order as exact single-loop SBO methods. BROS performs lower and auxiliary updates in randomized subspaces with a Rademacher bi-probe correction that recovers an unbiased Hessian-action estimator. We prove that BROS preserves the $\mathcal O(\varepsilon^{-2})$ sample complexity of MA-SOBA for finding an $\varepsilon$-stationary point under only standard assumptions. Experiments on hyper-data cleaning, data-mixture learning, hyper-representation learning, and ViT sample reweighting show that BROS reduces peak memory by up to 44.9% while closely matching full-space baseline performance.
format Preprint
id arxiv_https___arxiv_org_abs_2605_10288
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle BROS: Bias-Corrected Randomized Subspaces for Memory-Efficient Single-Loop Bilevel Optimization
Zhang, Hengrui
Kong, Boao
Zhang, Engao
Yuan, Kun
Machine Learning
Optimization and Control
90C30, 90C15, 68T07
Stochastic bilevel optimization (SBO) has become a standard framework for hyperparameter learning, data reweighting, representation learning, and data-mixture optimization in deep learning. Existing exact single-loop SBO methods and memory-efficient surrogate SBO methods either create severe memory pressure for large lower-level neural networks or lack competitive convergence guarantees under standard assumptions. In this paper, we propose BROS, a memory-efficient single-loop SBO method with the same convergence rate order as exact single-loop SBO methods. BROS performs lower and auxiliary updates in randomized subspaces with a Rademacher bi-probe correction that recovers an unbiased Hessian-action estimator. We prove that BROS preserves the $\mathcal O(\varepsilon^{-2})$ sample complexity of MA-SOBA for finding an $\varepsilon$-stationary point under only standard assumptions. Experiments on hyper-data cleaning, data-mixture learning, hyper-representation learning, and ViT sample reweighting show that BROS reduces peak memory by up to 44.9% while closely matching full-space baseline performance.
title BROS: Bias-Corrected Randomized Subspaces for Memory-Efficient Single-Loop Bilevel Optimization
topic Machine Learning
Optimization and Control
90C30, 90C15, 68T07
url https://arxiv.org/abs/2605.10288