Adadelta

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Author: Imran Shita-Bey (ias45), Dhruv Misra (dm668), Ifadhila Affia (ia284), Wenqu Zhang (wz473) (ChemE 6800 Fall 2024)

Stewards: Nathan Preuss, Wei-Han Chen, Tianqi Xiao, Guoqing Hu

Introduction

Optimization algorithms (“optimizers”) are analogous, in a way, to engines in cars. Just as different engines are designed to suit various driving requirements—some prioritizing speed, others efficiency—different optimizers are tailored to solve distinct types of problems. In machine learning, optimization algorithms like Adadelta adjust learning rates during neural network training in a somewhat-uniquely dynamic manner, enabling efficient and stable convergence. Introduced by Matthew D. Zeiler, Adadelta was developed to address the limitations of earlier adaptive methods, particularly Adagrad's vanishing learning rates in prolonged training sessions [1]. This innovation made Adadelta especially valuable as a method that does not need to manually tune learning rates, and therefore “appears robust to noisy gradient information, different model architecture choices, various data modalities and selection of hyperparameters” [1].

Similar to how even similarly sized cars can come with a myriad of engine types, other optimization algorithms, such as RMSprop [2], Adam [3], and Nadam [4], exist as well. Each algorithm has unique characteristics and trade-offs, much like how different engines excel in specific environments. For instance, Adam combines the strengths of momentum and adaptive learning rates to provide a versatile option for training models [3]. The existence of multiple optimizers emphasizes their role as the "engines" powering machine learning, allowing models to tackle a wide array of challenges.

Historically, gradient-based optimization techniques evolved to tackle challenges in training models with large parameter spaces, such as vanishing gradients and instability in updates [5]. Adadelta marked a critical milestone by automating learning rate adjustments, eliminating the need for manual hyperparameter tuning, and maintaining computational efficiency [1]. Its principles influenced the development of other algorithms like RMSprop and Adam, further showcasing how optimizers evolve to address specific needs, namely, adaptability.

The study of Adadelta and related optimization algorithms is driven by the goal of improving machine learning model training—minimizing loss functions effectively, reducing training time, and achieving better generalization. By understanding Adadelta’s mechanism and its relationship to other optimizers, researchers and practitioners can make informed decisions when selecting tools for specific machine learning tasks, optimizing performance across diverse applications [5].

Algorithm Discussion

Numerical Example

Problem Definition and Setup

Numerical Solution

Solution Graphical Analysis

Application

Natural Language Processing (NLP)

Deep Neural Networks

Conclusion

References

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

  1. ↑ Zeiler, M. D. (2012). ADADELTA: An Adaptive Learning Rate Method. arXiv preprint. Retrieved from [1](https://arxiv.org/abs/1212.5701).
  2. ↑ Tieleman, T., & Hinton, G. (2012). Lecture 6.5 - RMSprop: Divide the Gradient by a Running Average of its Recent Magnitude. COURSERA: Neural Networks for Machine Learning.
  3. ↑ Kingma, D. P., & Ba, J. (2014). Adam: A Method for Stochastic Optimization. arXiv preprint arXiv:1412.6980. Retrieved from [2](https://arxiv.org/abs/1412.6980).
  4. ↑ Dozat, T. (2016). Incorporating Nesterov Momentum into Adam. In Proceedings of the International Conference on Learning Representations (ICLR) 2016, Workshop Track. Retrieved from [3](https://openreview.net/forum?id=OM0jvwB8jIp57ZJjtNEZ).
  5. ↑ Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep Learning. MIT Press.
  6. ↑ TensorFlow Documentation. (n.d.). tf.keras.optimizers.Adadelta. Retrieved from [4](https://www.tensorflow.org/api_docs/python/tf/keras/optimizers/Adadelta).
  7. ↑ PyTorch Documentation. (n.d.). torch.optim.Adadelta. Retrieved from [5](https://pytorch.org/docs/stable/generated/torch.optim.Adadelta.html).
  8. ↑ Keras Documentation. (n.d.). Adadelta optimizer. Retrieved from [6](https://keras.io/api/optimizers/adadelta/).
  9. ↑ Wilson, A. C., Roelofs, R., Stern, M., Srebro, N., & Recht, B. (2017). The Marginal Value of Adaptive Gradient Methods in Machine Learning. Advances in Neural Information Processing Systems.
  10. ↑ Artificial Intelligence-Based Predictive Maintenance for Smart Manufacturing Systems. Alexandria Engineering Journal, 2024. Retrieved from [7](https://www.sciencedirect.com/science/article/pii/S1319157824001575).
  11. ↑ Liu, Z., & Hui, J. (2024). Predictive Maintenance for Industrial Systems: An Integrated Deep Learning and Event Log Approach. Emerald Studies in Reliability Engineering. Retrieved from [8](https://www.emerald.com/insight/content/doi/10.1108/sr-03-2024-0183/full/html).
  12. ↑ Chong, E., Han, C., & Park, F. C. (2017). Deep Learning Networks for Stock Market Analysis and Prediction: Methodology, Data Representations, and Case Studies. Expert Systems with Applications, vol. 83, 187–205. Retrieved from [9](https://www.sciencedirect.com/science/article/pii/S0378426617302435).
  13. ↑ Vaswani, A., Shazeer, N., Parmar, N., et al. (2017). Attention Is All You Need. Advances in Neural Information Processing Systems.
  14. ↑ Pascanu, R., Mikolov, T., & Bengio, Y. (2013). On the Difficulty of Training Recurrent Neural Networks. International Conference on Machine Learning.
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