Descending through a Crowded Valley - Benchmarking Deep Learning Optimizers
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Abstract (arXiv)
Choosing the optimizer is considered to be among the most crucial design decisions in deep learning, and it is not an easy one. The growing literature now lists hundreds of optimization methods. In the absence of clear theoretical guidance and conclusive empirical evidence, the decision is often made based on anecdotes. In this work, we aim to replace these anecdotes, if not with a conclusive ranking, then at least with evidence-backed heuristics. To do so, we perform an extensive, standardized benchmark of fifteen particularly popular deep learning optimizers while giving a concise overview of the wide range of possible choices. Analyzing more than 50,000 individual runs, we contribute the following three points: (i) Optimizer performance varies greatly across tasks. (ii) We observe that evaluating multiple optimizers with default parameters works approximately as well as tuning the hyperparameters of a single, fixed optimizer. (iii) While we cannot discern an optimization method clearly dominating across all tested tasks, we identify a significantly reduced subset of specific optimizers and parameter choices that generally lead to competitive results in our experiments: Adam remains a strong contender, with newer methods failing to significantly and consistently outperform it. Our open-sourced results are available as challenging and well-tuned baselines for more meaningful evaluations of novel optimization methods without requiring any further computational efforts.
Key facts. Cited by 118 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Jul 2020.
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Citing papers per year: 2021: 19; 2022: 28; 2023: 22; 2024: 16; 2025: 16; 2026: 17.
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- 2024Heavy-Tailed Class Imbalance and Why Adam Outperforms Gradient Descent on Language Modelscited by 78
- 2021Stochastic Training is Not Necessary for Generalizationcited by 63
- 2022VeLO: Training Versatile Learned Optimizers by Scaling Upcited by 57
- 2021Noether's Learning Dynamics: Role of Symmetry Breaking in Neural Networkscited by 47
- 2021Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networkscited by 43
- 2023No Train No Gain: Revisiting Efficient Training Algorithms For Transformer-based Language Modelscited by 41
- 2024Deconstructing What Makes a Good Optimizer for Language Modelscited by 40
- 2022Compute-Efficient Deep Learning: Algorithmic Trends and Opportunitiescited by 38
- 2025Straight to Zero: Why Linearly Decaying the Learning Rate to Zero Works Best for LLMscited 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
- 2025Accelerating Neural Network Training: An Analysis of the AlgoPerf Competitioncited by 30
38 more
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- 2021ViViT: Curvature access through the generalized Gauss-Newton's low-rank structurecited by 16
- 2025What Really Matters in Matrix-Whitening Optimizers?cited by 15
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- 2024An Adaptive Stochastic Gradient Method with Non-negative Gauss-Newton Stepsizescited by 10
- 2024Neural topology optimization: the good, the bad, and the uglycited by 9
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- 2023On the Disconnect Between Theory and Practice of Neural Networks: Limits of the NTK Perspectivecited by 6
- 2024MADA: Meta-Adaptive Optimizers through hyper-gradient Descentcited by 6
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- 2022Fast Benchmarking of Accuracy vs. Training Time with Cyclic Learning Ratescited by 5
50 most cited of 118 All 118 (JSON)
- 2026AURA: Angular Update Rate Adaptation for training complex-valued neural networks22 Sep 2026
- 2026Optimizers for Diffusion Models: A Controlled Benchmark19 Sep 2026
- 2026AdamX: Cosine similarity meets gradient descent10 Sep 2026
- 2026When Does Online Adaptation Pay on the Edge? A Leakage-Free Evaluation of Warmup, Learning-Rate Selection, and Resource Trade-offs for Time-Series Forecasting1 Sep 2026
- 2026On Cross-Validation for Hyperparameter Optimization of Deep Learning Image Classifiers10 Aug 2026
- 2026The Loss Does Not See the Basis, but Adam Does5 Aug 2026
- 2026LionVote: Per-Layer Learning Rate Adaptation for Lion10 Jul 2026
- 2026Beyond a Single Explanation of the Adam--SGD Gap12 Jun 2026
- 2026Large-scale empirical tuning and comparison of default optimizers for variational inference5 Jun 2026
- 2026Anon: Extrapolating Adaptivity Beyond SGD and Adam4 May 2026
- 2026Reasoning-Driven Synthetic Data Generation and Evaluation31 Mar 2026
- 2026Second-Order, First-Class: A Composable Stack for Curvature-Aware Training26 Mar 2026
38 more
- 2026Clarifying Shampoo: Adapting Spectral Descent to Stochasticity and the Parameter Trajectory10 Feb 2026
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- 2026Learning Rate Matters: Vanilla LoRA May Suffice for LLM Fine-tuning4 Feb 2026
- 2026The Effect of Mini-Batch Noise on the Implicit Bias of Adam2 Feb 2026
- 2026Optimal Learning Rate Schedule for Balancing Effort and Performance12 Jan 2026
- 2025Greedy Alignment Principle for Optimizer Selection6 Dec 2025
- 2025Design Criteria for SGD Preconditioners: Local Conditioning, Noise Floors, and Basin Stability24 Nov 2025
- 2025What Really Matters in Matrix-Whitening Optimizers?28 Oct 2025
- 2025Optimization Benchmark for Diffusion Models on Dynamical Systems22 Oct 2025
- 2025An Analysis of Optimizer Choice on Energy Efficiency and Performance in Neural Network Training16 Sep 2025
- 2025HOTSPOT-YOLO: A Lightweight Deep Learning Attention-Driven Model for Detecting Thermal Anomalies in Drone-Based Solar Photovoltaic Inspections26 Aug 2025
- 2025Consistency of Feature Attribution in Deep Learning Architectures for Multi-Omics30 Jul 2025
- 2025Fishers for Free? Approximating the Fisher Information Matrix by Recycling the Squared Gradient Accumulator24 Jul 2025
- 2025Revisiting Learning Rate Control2 Jul 2025
- 2025Rapid training of Hamiltonian graph networks using random features6 Jun 2025
- 2025How far away are truly hyperparameter-free learning algorithms?29 May 2025
- 2025Analysis of an Idealized Stochastic Polyak Method and its Application to Black-Box Model Distillation2 Apr 2025
- 2025Straight to Zero: Why Linearly Decaying the Learning Rate to Zero Works Best for LLMs21 Feb 2025
- 2025Accelerating Neural Network Training: An Analysis of the AlgoPerf Competition20 Feb 2025
- 2025Beyond Point Estimates: Distributional Uncertainty in Machine Learning Performance Evaluation28 Jan 2025
- 2025Celo: Training Versatile Learned Optimizers on a Compute Diet22 Jan 2025
- 2024MARINA-P: Superior Performance in Non-smooth Federated Optimization with Adaptive Stepsizes22 Dec 2024
- 2024Debiasing Mini-Batch Quadratics for Applications in Deep Learning18 Oct 2024
- 2024Unraveling the Hessian: A Key to Smooth Convergence in Loss Function Landscapes18 Sep 2024
- 2024Narrowing the Focus: Learned Optimizers for Pretrained Models17 Aug 2024
- 2024No learning rates needed: Introducing SALSA -- Stable Armijo Line Search Adaptation30 Jul 2024
- 2024Characterizing Dynamical Stability of Stochastic Gradient Descent in Overparameterized Learning29 Jul 2024
- 2024Neural topology optimization: the good, the bad, and the ugly19 Jul 2024
- 2024Deconstructing What Makes a Good Optimizer for Language Models10 Jul 2024
- 2024An Adaptive Stochastic Gradient Method with Non-negative Gauss-Newton Stepsizes5 Jul 2024
- 2024Hard ASH: Sparsity and the right optimizer make a continual learner26 Apr 2024
- 2024Learning truly monotone operators with applications to nonlinear inverse problems30 Mar 2024
- 2024Improving Line Search Methods for Large Scale Neural Network Training27 Mar 2024
- 2024Heavy-Tailed Class Imbalance and Why Adam Outperforms Gradient Descent on Language Models29 Feb 2024
- 2024Should I try multiple optimizers when fine-tuning pre-trained Transformers for NLP tasks? Should I tune their hyperparameters?10 Feb 2024
- 2024Breaking MLPerf Training: A Case Study on Optimizing BERT4 Feb 2024
- 2024MADA: Meta-Adaptive Optimizers through hyper-gradient Descent17 Jan 2024
- 2023Generalisable Agents for Neural Network Optimisation30 Nov 2023
50 newest of 118 All 118 (JSON)
- 2026Optimizers for Diffusion Models: A Controlled Benchmark19 Sep 2026
- 2025Optimization Benchmark for Diffusion Models on Dynamical Systems22 Oct 2025
- 2024Heavy-Tailed Class Imbalance and Why Adam Outperforms Gradient Descent on Language Modelscited by 78
- 2021Stochastic Training is Not Necessary for Generalizationcited by 63
- 2022VeLO: Training Versatile Learned Optimizers by Scaling Upcited by 57
- 2021Noether's Learning Dynamics: Role of Symmetry Breaking in Neural Networkscited by 47
- 2021Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networkscited by 43
- 2023No Train No Gain: Revisiting Efficient Training Algorithms For Transformer-based Language Modelscited by 41
- 2024Deconstructing What Makes a Good Optimizer for Language Modelscited by 40
- 2022Compute-Efficient Deep Learning: Algorithmic Trends and Opportunitiescited by 38
- 2025Straight to Zero: Why Linearly Decaying the Learning Rate to Zero Works Best for LLMscited 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
- 2025Accelerating Neural Network Training: An Analysis of the AlgoPerf Competitioncited by 30
12 most cited of 116 All 116 (JSON)
- 2026AURA: Angular Update Rate Adaptation for training complex-valued neural networks22 Sep 2026
- 2026AdamX: Cosine similarity meets gradient descent10 Sep 2026
- 2026When Does Online Adaptation Pay on the Edge? A Leakage-Free Evaluation of Warmup, Learning-Rate Selection, and Resource Trade-offs for Time-Series Forecasting1 Sep 2026
- 2026On Cross-Validation for Hyperparameter Optimization of Deep Learning Image Classifiers10 Aug 2026
- 2026The Loss Does Not See the Basis, but Adam Does5 Aug 2026
- 2026LionVote: Per-Layer Learning Rate Adaptation for Lion10 Jul 2026
- 2026Beyond a Single Explanation of the Adam--SGD Gap12 Jun 2026
- 2026Large-scale empirical tuning and comparison of default optimizers for variational inference5 Jun 2026
- 2026Anon: Extrapolating Adaptivity Beyond SGD and Adam4 May 2026
- 2026Reasoning-Driven Synthetic Data Generation and Evaluation31 Mar 2026
- 2026Second-Order, First-Class: A Composable Stack for Curvature-Aware Training26 Mar 2026
- 2026Clarifying Shampoo: Adapting Spectral Descent to Stochasticity and the Parameter Trajectory10 Feb 2026
12 newest of 116 All 116 (JSON)