# Bilevel Optimization for Neural Architecture Search

arXiv: https://arxiv.org/abs/2606.29582 · HTML: https://mlsanity.com/paper/2606.29582/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 62 of its 138 references that are in the map.
- First posted on arXiv 28 Jun 2026.

## Builds on (most cited first, 30 of 62)

- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Learning Transferable Architectures for Scalable Image Recognition](https://mlsanity.com/paper/1707.07012/) (2017)
- [MnasNet: Platform-Aware Neural Architecture Search for Mobile](https://mlsanity.com/paper/1807.11626/) (2018)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [Once-for-All: Train One Network and Specialize it for Efficient Deployment](https://mlsanity.com/paper/1908.09791/) (2019)
- [ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware](https://mlsanity.com/paper/1812.00332/) (2018)
- [FBNet: Hardware-Aware Efficient ConvNet Design via Differentiable Neural Architecture Search](https://mlsanity.com/paper/1812.03443/) (2018)
- [Pruning neural networks without any data by iteratively conserving synaptic flow](https://mlsanity.com/paper/2006.05467/) (2020)
- [NAS-Bench-201: Extending the Scope of Reproducible Neural Architecture Search](https://mlsanity.com/paper/2001.00326/) (2020)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Gradient-based Hyperparameter Optimization through Reversible Learning](https://mlsanity.com/paper/1502.03492/) (2015)
- [Large-Scale Evolution of Image Classifiers](https://mlsanity.com/paper/1703.01041/) (2017)
- [NAS-Bench-101: Towards Reproducible Neural Architecture Search](https://mlsanity.com/paper/1902.09635/) (2019)
- [Designing Neural Network Architectures using Reinforcement Learning](https://mlsanity.com/paper/1611.02167/) (2016)
- [PC-DARTS: Partial Channel Connections for Memory-Efficient Architecture Search](https://mlsanity.com/paper/1907.05737/) (2019)
- [Auto-DeepLab: Hierarchical Neural Architecture Search for Semantic Image Segmentation](https://mlsanity.com/paper/1901.02985/) (2019)
- [Neural Architecture Search without Training](https://mlsanity.com/paper/2006.04647/) (2020)
- [Progressive Differentiable Architecture Search: Bridging the Depth Gap between Search and Evaluation](https://mlsanity.com/paper/1904.12760/) (2019)
- [AutoFormer: Searching Transformers for Visual Recognition](https://mlsanity.com/paper/2107.00651/) (2021)
- [Understanding and Robustifying Differentiable Architecture Search](https://mlsanity.com/paper/1909.09656/) (2019)
- [Neural Architecture Search on ImageNet in Four GPU Hours: A Theoretically Inspired Perspective](https://mlsanity.com/paper/2102.11535/) (2021)
- [Efficient Multi-objective Neural Architecture Search via Lamarckian Evolution](https://mlsanity.com/paper/1804.09081/) (2018)
- [A Survey on Evolutionary Neural Architecture Search](https://mlsanity.com/paper/2008.10937/) (2020)
- [Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets](https://mlsanity.com/paper/1605.07079/) (2016)
- [Fair DARTS: Eliminating Unfair Advantages in Differentiable Architecture Search](https://mlsanity.com/paper/1911.12126/) (2019)
- [A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications](https://mlsanity.com/paper/1705.06270/) (2017)

## Built on by (most cited first, 2 of 2)

- [Designing Compact Neural Architectures via Neuron Gating and Mixed Activation](https://mlsanity.com/paper/2608.14443/) (2026)
- [LP-NAS: Linear Programming-based Neural Architecture Search](https://mlsanity.com/paper/2608.14472/) (2026)

## Abstract (arXiv)

Bilevel optimization has become an influential and widely adopted framework for addressing hierarchical optimization problems in machine learning, providing an effective approach to modeling the interaction between two levels of optimization, with applications such as hyperparameter tuning, meta-learning, adversarial training, and data poisoning. Neural Architecture Search (NAS), a subfield of hyperparameter optimization, is a prime example of a bilevel optimization problem, with architecture parameters optimized at the outer-level and network weights optimized at the inner level. This paper presents a structured overview of NAS through the lens of bilevel optimization. We categorize existing NAS approaches into two main classes: sampling-based methods, which search optimal architectures using different architecture samplers, and bilevel theory-based methods, which solve the architecture search problem using bilevel optimization principles. We further highlight our current research direction, wherein the bilevel NAS formulation is addressed through an auxiliary mathematical programming framework. This framework enables the systematic integration of second-order information from the model's training loss function and ensures the optimality of the model parameters while modifying architecture parameters. By simultaneously updating the architecture and model parameters along their respective optimal descent directions derived from the auxiliary mathematical program, these methods achieve more principled and theoretically consistent results. The same auxiliary program can also be used for simultaneous hyperparameter and model fine-tuning. A comparative analysis shows that bilevel theory-based approaches generally outperform sampling-based methods, both in accuracy and efficiency.