# CAdam: Confidence-Based Optimization for Online Learning

arXiv: https://arxiv.org/abs/2411.19647 · HTML: https://mlsanity.com/paper/2411.19647/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 51 references that are in the map.
- First posted on arXiv 29 Nov 2024.

## Builds on (most cited first, 30 of 32)

- [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)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Wide & Deep Learning for Recommender Systems](https://mlsanity.com/paper/1606.07792/) (2016)
- [DeepFM: A Factorization-Machine based Neural Network for CTR Prediction](https://mlsanity.com/paper/1703.04247/) (2017)
- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Symbolic Discovery of Optimization Algorithms](https://mlsanity.com/paper/2302.06675/) (2023)
- [Deep & Cross Network for Ad Click Predictions](https://mlsanity.com/paper/1708.05123/) (2017)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [A Simple Convergence Proof of Adam and Adagrad](https://mlsanity.com/paper/2003.02395/) (2020)
- [Product-based Neural Networks for User Response Prediction](https://mlsanity.com/paper/1611.00144/) (2016)
- [Adam Can Converge Without Any Modification On Update Rules](https://mlsanity.com/paper/2208.09632/) (2022)
- [Convergence of Adam Under Relaxed Assumptions](https://mlsanity.com/paper/2304.13972/) (2023)
- [BARS: Towards Open Benchmarking for Recommender Systems](https://mlsanity.com/paper/2205.09626/) (2022)
- [Open Benchmarking for Click-Through Rate Prediction](https://mlsanity.com/paper/2009.05794/) (2020)
- [Cautious Optimizers: Improving Training with One Line of Code](https://mlsanity.com/paper/2411.16085/) (2024)
- [Closing the Gap Between the Upper Bound and the Lower Bound of Adam's Iteration Complexity](https://mlsanity.com/paper/2310.17998/) (2023)
- [A new regret analysis for Adam-type algorithms](https://mlsanity.com/paper/2003.09729/) (2020)
- [On the Convergence of Adam under Non-uniform Smoothness: Separability from SGDM and Beyond](https://mlsanity.com/paper/2403.15146/) (2024)
- [Adaptive Online Incremental Learning for Evolving Data Streams](https://mlsanity.com/paper/2201.01633/) (2022)
- [Automated Data Denoising for Recommendation](https://mlsanity.com/paper/2305.07070/) (2023)
- [Online Robust and Adaptive Learning from Data Streams](https://mlsanity.com/paper/2007.12160/) (2020)

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

- [Cautious Weight Decay](https://mlsanity.com/paper/2510.12402/) (2025)
- [Evolution of Optimization Methods: Algorithms, Scenarios, and Evaluations](https://mlsanity.com/paper/2604.12968/) (2026)

## Abstract (arXiv)

Modern recommendation systems frequently employ online learning to dynamically update their models with freshly collected data. The most commonly used optimizer for updating neural networks in these contexts is the Adam optimizer, which integrates momentum (mt) and adaptive learning rate (vt). However, the volatile nature of online learning data, characterized by its frequent distribution shifts and presence of noise, poses significant challenges to Adam's standard optimization process: (1) Adam may use outdated momentum and the average of squared gradients, resulting in slower adaptation to distribution changes, and (2) Adam's performance is adversely affected by data noise. To mitigate these issues, we introduce CAdam, a confidence-based optimization strategy that assesses the consistency between the momentum and the gradient for each parameter dimension before deciding on updates. If momentum and gradient are in sync, CAdam proceeds with parameter updates according to Adam's original formulation; if not, it temporarily withholds updates and monitors potential shifts in data distribution in subsequent iterations. This method allows CAdam to distinguish between the true distributional shifts and mere noise, and to adapt more quickly to new data distributions. In various settings with distribution shift or noise, our experiments demonstrate that CAdam surpasses other well-known optimizers, including the original Adam. Furthermore, in large-scale A/B testing within a live recommendation system, CAdam significantly enhances model performance compared to Adam, leading to substantial increases in the system's gross merchandise volume (GMV).