Learned Optimizers that Scale and Generalize
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Abstract (arXiv)
Learning to learn has emerged as an important direction for achieving artificial intelligence. Two of the primary barriers to its adoption are an inability to scale to larger problems and a limited ability to generalize to new tasks. We introduce a learned gradient descent optimizer that generalizes well to new tasks, and which has significantly reduced memory and computation overhead. We achieve this by introducing a novel hierarchical RNN architecture, with minimal per-parameter overhead, augmented with additional architectural features that mirror the known structure of optimization tasks. We also develop a meta-training ensemble of small, diverse optimization tasks capturing common properties of loss landscapes. The optimizer learns to outperform RMSProp/ADAM on problems in this corpus. More importantly, it performs comparably or better when applied to small convolutional neural networks, despite seeing no neural networks in its meta-training set. Finally, it generalizes to train Inception V3 and ResNet V2 architectures on the ImageNet dataset for thousands of steps, optimization problems that are of a vastly different scale than those it was trained on. We release an open source implementation of the meta-training algorithm.
Key facts. Cited by 109 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Mar 2017.
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Citing papers per year: 2021: 29; 2022: 19; 2023: 20; 2024: 14; 2025: 17; 2026: 10.
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- 2023Symbolic Discovery of Optimization Algorithmscited by 423
- 2021Learning to Optimize: A Primer and A Benchmarkcited by 206
- 2022A Comprehensive Survey of Few-shot Learning: Evolution, Applications, Challenges, and Opportunitiescited by 162
- 2021Parameter Prediction for Unseen Deep Architecturescited by 89
- 2022Learning to Learn with Generative Models of Neural Network Checkpointscited by 85
- 2022Tutorial on amortized optimizationcited by 83
- 2021Gradients are Not All You Needcited by 82
- 2023Advances and Challenges in Meta-Learning: A Technical Reviewcited by 65
- 2024Graph Neural Networks for Learning Equivariant Representations of Neural Networkscited by 59
- 2022VeLO: Training Versatile Learned Optimizers by Scaling Upcited by 57
- 2021Unbiased Gradient Estimation in Unrolled Computation Graphs with Persistent Evolution Strategiescited by 52
- 2021Bootstrapped Meta-Learningcited by 45
38 more
- 2021Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detectioncited by 34
- 2022Practical tradeoffs between memory, compute, and performance in learned optimizerscited by 32
- 2022A Closer Look at Learned Optimization: Stability, Robustness, and Inductive Biasescited by 30
- 2024G3R: Gradient Guided Generalizable Reconstructioncited by 29
- 2022Gradient-based Bi-level Optimization for Deep Learning: A Surveycited by 26
- 2024Universal Neural Functionalscited by 25
- 2021A Generalizable Approach to Learning Optimizerscited by 23
- 2021How to Train Your MAML to Excel in Few-Shot Classificationcited by 22
- 2023Improving physics-informed neural networks with meta-learned optimizationcited by 19
- 2022Symbolic Learning to Optimize: Towards Interpretability and Scalabilitycited by 16
- 2024In-context Exploration-Exploitation for Reinforcement Learningcited by 16
- 2022Landscape Learning for Neural Network Inversioncited by 15
- 2023B2Opt: Learning to Optimize Black-box Optimization with Little Budgetcited by 15
- 2021Benchmarking Safety Monitors for Image Classifiers with Machine Learningcited by 14
- 2024Can Learned Optimization Make Reinforcement Learning Less Difficult?cited by 14
- 2021Training Learned Optimizers with Randomly Initialized Learned Optimizerscited by 13
- 2021Searching for Robustness: Loss Learning for Noisy Classification Taskscited by 13
- 2022Transformer-Based Learned Optimizationcited by 13
- 2023Towards Constituting Mathematical Structures for Learning to Optimizecited by 13
- 2021Learn2Hop: Learned Optimization on Rough Landscapescited by 12
- 2023Learning to Optimize for Reinforcement Learningcited by 12
- 2021How to decay your learning ratecited by 11
- 2024Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Processcited by 11
- 2025LIFe-GoM: Generalizable Human Rendering with Learned Iterative Feedback Over Multi-Resolution Gaussians-on-Meshcited by 11
- 2025QuickSplat: Fast 3D Surface Reconstruction via Learned Gaussian Initializationcited by 11
- 2021Meta-Learning Bidirectional Update Rulescited by 10
- 2021Neural Fixed-Point Acceleration for Convex Optimizationcited by 10
- 2023Rapid Network Adaptation: Learning to Adapt Neural Networks Using Test-Time Feedbackcited by 10
- 2021MetricOpt: Learning to Optimize Black-Box Evaluation Metricscited by 9
- 2021Learning an Explicit Hyperparameter Prediction Function Conditioned on Taskscited by 9
- 2022Amortized Proximal Optimizationcited by 9
- 2023Mnemosyne: Learning to Train Transformers with Transformerscited by 9
- 2023Learning to Generalize Provably in Learning to Optimizecited by 8
- 2024Adaptive Non-uniform Timestep Sampling for Accelerating Diffusion Model Trainingcited by 8
- 2022Teaching Networks to Solve Optimization Problemscited by 7
- 2022Meta Mirror Descent: Optimiser Learning for Fast Convergencecited by 7
- 2023Low-Variance Gradient Estimation in Unrolled Computation Graphs with ES-Singlecited by 7
- 2023Deep Model Predictive Optimizationcited by 7
50 most cited of 109 All 109 (JSON)
- 2026Learned Preconditioning for a Primal-Dual Interior-Point Method28 Sep 2026
- 2026SOLAR: A State-Driven Online Learning Rate Scheduler for LLM Pretraining28 Sep 2026
- 2026FunL2O: LLM-Guided Feature Function Design for Learning to Optimize29 Jul 2026
- 2026NeurGO: Learning to Generate Elite Candidates for Meta-Black-Box Expensive Optimization26 Jul 2026
- 2026Efficient Long-Horizon Learning for Learned Optimization7 Jul 2026
- 2026FlowBender: Feedback-Aware Training for Self-Correcting Conditional Flows18 Jun 2026
- 2026Learn2Splat: Extending the Horizon of Learned 3DGS Optimization15 May 2026
- 2026Celo2: Towards Learned Optimization Free Lunch22 Feb 2026
- 2026Learning to Discover Iterative Spectral Algorithms10 Feb 2026
- 2026Majorization-Minimization Networks for Inverse Problems: An Application to EEG Imaging23 Jan 2026
- 2025Greedy Alignment Principle for Optimizer Selection6 Dec 2025
- 2025Evolving Deep Learning Optimizers5 Dec 2025
38 more
- 2025Neural Coherence : Find higher performance to out-of-distribution tasks from few samples5 Dec 2025
- 2025A Semi-amortized Lifted Learning-to-Optimize Masked (SALLO-M) Transformer Model for Scalable and Generalizable Beamforming15 Oct 2025
- 2025Learning Regularizers: Learning Optimizers that can Regularize10 Oct 2025
- 2025Learning a Zeroth-Order Optimizer for Fine-Tuning LLMs1 Oct 2025
- 2025L-SR1: Learned Symmetric-Rank-One Preconditioning17 Aug 2025
- 2025Learning from Oblivion: Predicting Knowledge Overflowed Weights via Retrodiction of Forgetting7 Aug 2025
- 2025Towards Robust Learning to Optimize with Theoretical Guarantees17 Jun 2025
- 2025QuickSplat: Fast 3D Surface Reconstruction via Learned Gaussian Initialization8 May 2025
- 2025Scalable Meta-Learning via Mixed-Mode Differentiation1 May 2025
- 2025Improving Learning to Optimize Using Parameter Symmetries21 Apr 2025
- 2025On the Duality between Gradient Transformations and Adapters19 Feb 2025
- 2025LIFe-GoM: Generalizable Human Rendering with Learned Iterative Feedback Over Multi-Resolution Gaussians-on-Mesh13 Feb 2025
- 2025Universal Sequence Preconditioning10 Feb 2025
- 2025Celo: Training Versatile Learned Optimizers on a Compute Diet22 Jan 2025
- 2025Meta-Sparsity: Learning Optimal Sparse Structures in Multi-task Networks through Meta-learning21 Jan 2025
- 2024Adaptive Non-uniform Timestep Sampling for Accelerating Diffusion Model Training15 Nov 2024
- 2024A Generalization Result for Convergence in Learning-to-Optimize10 Oct 2024
- 2024G3R: Gradient Guided Generalizable Reconstruction28 Sep 2024
- 2024Narrowing the Focus: Learned Optimizers for Pretrained Models17 Aug 2024
- 2024Learning to Learn without Forgetting using Attention6 Aug 2024
- 2024Can Learned Optimization Make Reinforcement Learning Less Difficult?9 Jul 2024
- 2024μLO: Compute-Efficient Meta-Generalization of Learned Optimizers31 May 2024
- 2024From Learning to Optimize to Learning Optimization Algorithms28 May 2024
- 2024Graph Neural Networks for Learning Equivariant Representations of Neural Networks18 Mar 2024
- 2024In-context Exploration-Exploitation for Reinforcement Learning11 Mar 2024
- 2024Dynamic Memory Based Adaptive Optimization23 Feb 2024
- 2024Universal Neural Functionals7 Feb 2024
- 2024MADA: Meta-Adaptive Optimizers through hyper-gradient Descent17 Jan 2024
- 2024Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Process6 Jan 2024
- 2023Meta-learning Optimizers for Communication-Efficient Learning2 Dec 2023
- 2023Generalisable Agents for Neural Network Optimisation30 Nov 2023
- 2023Is Scaling Learned Optimizers Worth It? Evaluating The Value of VeLO's 4000 TPU Months27 Oct 2023
- 2023Deep Model Predictive Optimization6 Oct 2023
- 2023Rapid Network Adaptation: Learning to Adapt Neural Networks Using Test-Time Feedback27 Sep 2023
- 2023Advances and Challenges in Meta-Learning: A Technical Review10 Jul 2023
- 2023Fast Context Adaptation in Cost-Aware Continual Learning6 Jun 2023
- 2023Towards Constituting Mathematical Structures for Learning to Optimize29 May 2023
- 2023Stochastic Unrolled Federated Learning24 May 2023
50 newest of 109 All 109 (JSON)
- 2023Symbolic Discovery of Optimization Algorithmscited by 423
- 2021Learning to Optimize: A Primer and A Benchmarkcited by 206
- 2022A Comprehensive Survey of Few-shot Learning: Evolution, Applications, Challenges, and Opportunitiescited by 162
- 2021Parameter Prediction for Unseen Deep Architecturescited by 89
- 2022Learning to Learn with Generative Models of Neural Network Checkpointscited by 85
- 2022Tutorial on amortized optimizationcited by 83
- 2021Gradients are Not All You Needcited by 82
- 2023Advances and Challenges in Meta-Learning: A Technical Reviewcited by 65
- 2024Graph Neural Networks for Learning Equivariant Representations of Neural Networkscited by 59
- 2022VeLO: Training Versatile Learned Optimizers by Scaling Upcited by 57
- 2021Unbiased Gradient Estimation in Unrolled Computation Graphs with Persistent Evolution Strategiescited by 52
- 2021Bootstrapped Meta-Learningcited by 45
12 most cited of 107 All 107 (JSON)
- 2026Learned Preconditioning for a Primal-Dual Interior-Point Method28 Sep 2026
- 2026SOLAR: A State-Driven Online Learning Rate Scheduler for LLM Pretraining28 Sep 2026
- 2026FunL2O: LLM-Guided Feature Function Design for Learning to Optimize29 Jul 2026
- 2026NeurGO: Learning to Generate Elite Candidates for Meta-Black-Box Expensive Optimization26 Jul 2026
- 2026Efficient Long-Horizon Learning for Learned Optimization7 Jul 2026
- 2026FlowBender: Feedback-Aware Training for Self-Correcting Conditional Flows18 Jun 2026
- 2026Learn2Splat: Extending the Horizon of Learned 3DGS Optimization15 May 2026
- 2026Celo2: Towards Learned Optimization Free Lunch22 Feb 2026
- 2026Learning to Discover Iterative Spectral Algorithms10 Feb 2026
- 2026Majorization-Minimization Networks for Inverse Problems: An Application to EEG Imaging23 Jan 2026
- 2025Greedy Alignment Principle for Optimizer Selection6 Dec 2025
- 2025Evolving Deep Learning Optimizers5 Dec 2025
12 newest of 107 All 107 (JSON)