# A General Descent Aggregation Framework for Gradient-based Bi-level Optimization

arXiv: https://arxiv.org/abs/2102.07976 · HTML: https://mlsanity.com/paper/2102.07976/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 57 references that are in the map.
- First posted on arXiv 16 Feb 2021.

## Builds on (most cited first, 30 of 30)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [FBNet: Hardware-Aware Efficient ConvNet Design via Differentiable Neural Architecture Search](https://mlsanity.com/paper/1812.03443/) (2018)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Meta-SGD: Learning to Learn Quickly for Few-Shot Learning](https://mlsanity.com/paper/1707.09835/) (2017)
- [Gradient-based Hyperparameter Optimization through Reversible Learning](https://mlsanity.com/paper/1502.03492/) (2015)
- [Optimizing Millions of Hyperparameters by Implicit Differentiation](https://mlsanity.com/paper/1911.02590/) (2019)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [Forward and Reverse Gradient-Based Hyperparameter Optimization](https://mlsanity.com/paper/1703.01785/) (2017)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [Truncated Back-propagation for Bilevel Optimization](https://mlsanity.com/paper/1810.10667/) (2018)
- [On the Iteration Complexity of Hypergradient Computation](https://mlsanity.com/paper/2006.16218/) (2020)
- [Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond](https://mlsanity.com/paper/2101.11517/) (2021)
- [On the Convergence Theory of Gradient-Based Model-Agnostic Meta-Learning Algorithms](https://mlsanity.com/paper/1908.10400/) (2019)
- [Few-Shot Image Recognition by Predicting Parameters from Activations](https://mlsanity.com/paper/1706.03466/) (2017)
- [Self-Tuning Networks: Bilevel Optimization of Hyperparameters using Structured Best-Response Functions](https://mlsanity.com/paper/1903.03088/) (2019)
- [A Generic First-Order Algorithmic Framework for Bi-Level Programming Beyond Lower-Level Singleton](https://mlsanity.com/paper/2006.04045/) (2020)
- [Stochastic Hyperparameter Optimization through Hypernetworks](https://mlsanity.com/paper/1802.09419/) (2018)
- [A mathematical model for automatic differentiation in machine learning](https://mlsanity.com/paper/2006.02080/) (2020)
- [Implicit differentiation of Lasso-type models for hyperparameter optimization](https://mlsanity.com/paper/2002.08943/) (2020)
- [TF-NAS: Rethinking Three Search Freedoms of Latency-Constrained Differentiable Neural Architecture Search](https://mlsanity.com/paper/2008.05314/) (2020)
- [Bilevel parameter learning for higher-order total variation regularisation models](https://mlsanity.com/paper/1508.07243/) (2015)
- [Investigating Task-driven Latent Feasibility for Nonconvex Image Modeling](https://mlsanity.com/paper/1910.08242/) (2019)
- [RePr: Improved Training of Convolutional Filters](https://mlsanity.com/paper/1811.07275/) (2018)
- [Two-level value function approach to nonsmooth optimistic and pessimistic bilevel programs](https://mlsanity.com/paper/1711.11127/) (2017)

## Built on by (most cited first, 28 of 28)

- [On Penalty-based Bilevel Gradient Descent Method](https://mlsanity.com/paper/2302.05185/) (2023)
- [LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discovery](https://mlsanity.com/paper/2405.09783/) (2024)
- [Unsupervised Misaligned Infrared and Visible Image Fusion via Cross-Modality Image Generation and Registration](https://mlsanity.com/paper/2205.11876/) (2022)
- [SEAL: Safety-enhanced Aligned LLM Fine-tuning via Bilevel Data Selection](https://mlsanity.com/paper/2410.07471/) (2024)
- [Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyond](https://mlsanity.com/paper/2110.00455/) (2021)
- [A Task-guided, Implicitly-searched and Meta-initialized Deep Model for Image Fusion](https://mlsanity.com/paper/2305.15862/) (2023)
- [Principled Penalty-based Methods for Bilevel Reinforcement Learning and RLHF](https://mlsanity.com/paper/2402.06886/) (2024)
- [Neural Preset for Color Style Transfer](https://mlsanity.com/paper/2303.13511/) (2023)
- [BiAdam: Fast Adaptive Bilevel Optimization Methods](https://mlsanity.com/paper/2106.11396/) (2021)
- [Enhanced Bilevel Optimization via Bregman Distance](https://mlsanity.com/paper/2107.12301/) (2021)
- [Averaged Method of Multipliers for Bi-Level Optimization without Lower-Level Strong Convexity](https://mlsanity.com/paper/2302.03407/) (2023)
- [Value-Function-based Sequential Minimization for Bi-level Optimization](https://mlsanity.com/paper/2110.04974/) (2021)
- [Bilevel Optimization with a Lower-level Contraction: Optimal Sample Complexity without Warm-start](https://mlsanity.com/paper/2202.03397/) (2022)
- [A Generalized Physical-knowledge-guided Dynamic Model for Underwater Image Enhancement](https://mlsanity.com/paper/2308.05447/) (2023)
- [Constrained Bi-Level Optimization: Proximal Lagrangian Value function Approach and Hessian-free Algorithm](https://mlsanity.com/paper/2401.16164/) (2024)
- [Moreau Envelope for Nonconvex Bi-Level Optimization: A Single-loop and Hessian-free Solution Strategy](https://mlsanity.com/paper/2405.09927/) (2024)
- [Value Function Based Difference-of-Convex Algorithm for Bilevel Hyperparameter Selection Problems](https://mlsanity.com/paper/2206.05976/) (2022)
- [A First-Order Multi-Gradient Algorithm for Multi-Objective Bi-Level Optimization](https://mlsanity.com/paper/2401.09257/) (2024)
- [Optimization-Derived Learning with Essential Convergence Analysis of Training and Hyper-training](https://mlsanity.com/paper/2206.07875/) (2022)
- [Learning with Constraint Learning: New Perspective, Solution Strategy and Various Applications](https://mlsanity.com/paper/2307.15257/) (2023)
- [Learning Reward and Policy Jointly from Demonstration and Preference Improves Alignment](https://mlsanity.com/paper/2406.06874/) (2024)
- [Revisiting GANs by Best-Response Constraint: Perspective, Methodology, and Application](https://mlsanity.com/paper/2205.10146/) (2022)
- [Hierarchical Optimization-Derived Learning](https://mlsanity.com/paper/2302.05587/) (2023)
- [Little Strokes Fell Great Oaks: Boosting the Hierarchical Features for Multi-exposure Image Fusion](https://mlsanity.com/paper/2404.06033/) (2024)
- [Penalty-Based First-Order Methods for Bilevel Optimization with Minimax and Constrained Lower-Level Problems](https://mlsanity.com/paper/2605.08006/) (2026)
- [Motion-Scenario Decoupling for Rat-Aware Video Position Prediction: Strategy and Benchmark](https://mlsanity.com/paper/2305.18310/) (2023)
- [BLO-Inst: Bi-Level Optimization Based Alignment of YOLO and SAM for Robust Instance Segmentation](https://mlsanity.com/paper/2601.22061/) (2026)
- [S3LDBO: A Snapshot Single-Loop Algorithm for Decentralized Bilevel Optimization](https://mlsanity.com/paper/2605.31311/) (2026)

## Abstract (arXiv)

In recent years, a variety of gradient-based methods have been developed to solve Bi-Level Optimization (BLO) problems in machine learning and computer vision areas. However, the theoretical correctness and practical effectiveness of these existing approaches always rely on some restrictive conditions (e.g., Lower-Level Singleton, LLS), which could hardly be satisfied in real-world applications. Moreover, previous literature only proves theoretical results based on their specific iteration strategies, thus lack a general recipe to uniformly analyze the convergence behaviors of different gradient-based BLOs. In this work, we formulate BLOs from an optimistic bi-level viewpoint and establish a new gradient-based algorithmic framework, named Bi-level Descent Aggregation (BDA), to partially address the above issues. Specifically, BDA provides a modularized structure to hierarchically aggregate both the upper- and lower-level subproblems to generate our bi-level iterative dynamics. Theoretically, we establish a general convergence analysis template and derive a new proof recipe to investigate the essential theoretical properties of gradient-based BLO methods. Furthermore, this work systematically explores the convergence behavior of BDA in different optimization scenarios, i.e., considering various solution qualities (i.e., global/local/stationary solution) returned from solving approximation subproblems. Extensive experiments justify our theoretical results and demonstrate the superiority of the proposed algorithm for hyper-parameter optimization and meta-learning tasks. Source code is available at https://github.com/vis-opt-group/BDA.