mlsanityData to 14 Oct 2026

Sharper Analysis of Single-Loop Methods for Bilevel Optimization

arXiv 2607.10263 ↗First posted 11 Jul 2026cs.LGcited by 0

On the map: Deep reinforcement learning methods → RL theory and sample complexity

Abstract (arXiv)

Bilevel optimization underpins many machine learning applications, including hyperparameter optimization, meta-learning, neural architecture search, and reinforcement learning. While hypergradient-based methods have advanced significantly, a gap persists between theoretical guarantees and practical single-loop implementations required for efficiency. We bridge this gap by establishing sharper convergence results for single-loop approximate implicit differentiation (AID) and iterative differentiation (ITD) methods, leveraging our proposed analytical framework, decoupled norm analysis (DNA). For AID, we improve the convergence rate from O(kappa6/K) to O(kappa5/K), where kappa is the condition number of the inner-level problem. For ITD, we prove that the asymptotic error is O(kappa2), exactly matching the known lower bound and improving upon the previous O(kappa3) guarantee. Numerical experiments on synthetic and real tasks corroborate our theoretical findings.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods. Builds on 28 of its 34 references that are in the map. First posted on arXiv 11 Jul 2026.

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28 of 34 references.

References · 28

  1. 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,897
  2. 2018DARTS: Differentiable Architecture Searchcited by 1,798
  3. 2018Learning to Reweight Examples for Robust Deep Learningcited by 675
  4. 2018Bilevel Programming for Hyperparameter Optimization and Meta-Learningcited by 405
  5. 2015Gradient-based Hyperparameter Optimization through Reversible Learningcited by 360
  6. 2018Approximation Methods for Bilevel Programmingcited by 236
  7. 2017Forward and Reverse Gradient-Based Hyperparameter Optimizationcited by 234
  8. 2016Hyperparameter optimization with approximate gradientcited by 233
  9. 2020Bilevel Optimization: Convergence Analysis and Enhanced Designcited by 222
  10. 2018Truncated Back-propagation for Bilevel Optimizationcited by 190
  11. 2020On the Iteration Complexity of Hypergradient Computationcited by 155
  12. 2017Lower Bounds for Finding Stationary Points Icited by 126
16 more
  1. 2023A Fully First-Order Method for Stochastic Bilevel Optimizationcited by 100
  2. 2024SEAL: Safety-enhanced Aligned LLM Fine-tuning via Bilevel Data Selectioncited by 64
  3. 2021Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyondcited by 63
  4. 2020MiLeNAS: Efficient Neural Architecture Search via Mixed-Level Reformulationcited by 57
  5. 2024Principled Penalty-based Methods for Bilevel Reinforcement Learning and RLHFcited by 41
  6. 2019Bi-level Actor-Critic for Multi-agent Coordinationcited by 39
  7. 2023On Finding Small Hyper-Gradients in Bilevel Optimization: Hardness Results and Improved Analysiscited by 39
  8. 2022Will Bilevel Optimizers Benefit from Loopscited by 36
  9. 2021Stability and Generalization of Bilevel Programming in Hyperparameter Optimizationcited by 31
  10. 2020On the Global Optimality of Model-Agnostic Meta-Learningcited by 21
  11. 2023Near-Optimal Nonconvex-Strongly-Convex Bilevel Optimization with Fully First-Order Oraclescited by 17
  12. 2023Making Scalable Meta Learning Practicalcited by 17
  13. 2024Moreau Envelope for Nonconvex Bi-Level Optimization: A Single-loop and Hessian-free Solution Strategycited by 16
  14. 2021Relational Experience Replay: Continual Learning by Adaptively Tuning Task-wise Relationshipcited by 12
  15. 2025Efficient Curvature-Aware Hypergradient Approximation for Bilevel Optimizationcited by 3
  16. 2025qNBO: quasi-Newton Meets Bilevel Optimizationcited by 2

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