# AutoLRS: Automatic Learning-Rate Schedule by Bayesian Optimization on the Fly

arXiv: https://arxiv.org/abs/2105.10762 · HTML: https://mlsanity.com/paper/2105.10762/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 59 references that are in the map.
- First posted on arXiv 22 May 2021.

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Aligning Books and Movies: Towards Story-like Visual Explanations by Watching Movies and Reading Books](https://mlsanity.com/paper/1506.06724/) (2015)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [BOHB: Robust and Efficient Hyperparameter Optimization at Scale](https://mlsanity.com/paper/1807.01774/) (2018)
- [Population Based Training of Neural Networks](https://mlsanity.com/paper/1711.09846/) (2017)
- [Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers](https://mlsanity.com/paper/1811.04918/) (2018)
- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [Three Factors Influencing Minima in SGD](https://mlsanity.com/paper/1711.04623/) (2017)
- [One weird trick for parallelizing convolutional neural networks](https://mlsanity.com/paper/1404.5997/) (2014)
- [Deep Learning without Poor Local Minima](https://mlsanity.com/paper/1605.07110/) (2016)
- [Forward and Reverse Gradient-Based Hyperparameter Optimization](https://mlsanity.com/paper/1703.01785/) (2017)
- [A disciplined approach to neural network hyper-parameters: Part 1 -- learning rate, batch size, momentum, and weight decay](https://mlsanity.com/paper/1803.09820/) (2018)
- [Non-stochastic Best Arm Identification and Hyperparameter Optimization](https://mlsanity.com/paper/1502.07943/) (2015)
- [A System for Massively Parallel Hyperparameter Tuning](https://mlsanity.com/paper/1810.05934/) (2018)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)

## Built on by (most cited first, 14 of 14)

- [Optimal Linear Decay Learning Rate Schedules and Further Refinements](https://mlsanity.com/paper/2310.07831/) (2023)
- [A Multi-Power Law for Loss Curve Prediction Across Learning Rate Schedules](https://mlsanity.com/paper/2503.12811/) (2025)
- [Rethinking Learning Rate Tuning in the Era of Large Language Models](https://mlsanity.com/paper/2309.08859/) (2023)
- [Selecting and Composing Learning Rate Policies for Deep Neural Networks](https://mlsanity.com/paper/2210.12936/) (2022)
- [An Automatic Learning Rate Schedule Algorithm for Achieving Faster Convergence and Steeper Descent](https://mlsanity.com/paper/2310.11291/) (2023)
- [AutoDrop: Training Deep Learning Models with Automatic Learning Rate Drop](https://mlsanity.com/paper/2111.15317/) (2021)
- [Studying K-FAC Heuristics by Viewing Adam through a Second-Order Lens](https://mlsanity.com/paper/2310.14963/) (2023)
- [Crafting Efficient Fine-Tuning Strategies for Large Language Models](https://mlsanity.com/paper/2407.13906/) (2024)
- [Boosting Deep Ensembles with Learning Rate Tuning](https://mlsanity.com/paper/2410.07564/) (2024)
- [LRTuner: A Learning Rate Tuner for Deep Neural Networks](https://mlsanity.com/paper/2105.14526/) (2021)
- [Active-Learning-as-a-Service: An Automatic and Efficient MLOps System for Data-Centric AI](https://mlsanity.com/paper/2207.09109/) (2022)
- [Dynamic Learning Rate Scheduling based on Loss Changes Leads to Faster Convergence](https://mlsanity.com/paper/2512.14527/) (2025)
- [What do near-optimal learning rate schedules look like?](https://mlsanity.com/paper/2603.10301/) (2026)
- [SOLAR: A State-Driven Online Learning Rate Scheduler for LLM Pretraining](https://mlsanity.com/paper/2609.34681/) (2026)

## Abstract (arXiv)

The learning rate (LR) schedule is one of the most important hyper-parameters needing careful tuning in training DNNs. However, it is also one of the least automated parts of machine learning systems and usually costs significant manual effort and computing. Though there are pre-defined LR schedules and optimizers with adaptive LR, they introduce new hyperparameters that need to be tuned separately for different tasks/datasets. In this paper, we consider the question: Can we automatically tune the LR over the course of training without human involvement? We propose an efficient method, AutoLRS, which automatically optimizes the LR for each training stage by modeling training dynamics. AutoLRS aims to find an LR applied to every τ steps that minimizes the resulted validation loss. We solve this black-box optimization on the fly by Bayesian optimization (BO). However, collecting training instances for BO requires a system to evaluate each LR queried by BO's acquisition function for τ steps, which is prohibitively expensive in practice. Instead, we apply each candidate LR for only τ'llτ steps and train an exponential model to predict the validation loss after τ steps. This mutual-training process between BO and the loss-prediction model allows us to limit the training steps invested in the BO search. We demonstrate the advantages and the generality of AutoLRS through extensive experiments of training DNNs for tasks from diverse domains using different optimizers. The LR schedules auto-generated by AutoLRS lead to a speedup of 1.22×, 1.43×, and 1.5× when training ResNet-50, Transformer, and BERT, respectively, compared to the LR schedules in their original papers, and an average speedup of 1.31× over state-of-the-art heavily-tuned LR schedules.