Adaptive Optimization Algorithms for Deep Neural Networks under Non-Convex Stochastic Objectives
Keywords:
Adaptive optimization, deep neural networks, non-convex stochastic optimization, distributed training, robustness, fairness, governance, sustainability, sociotechnical infrastructureAbstract
The optimization of deep neural networks under non-convex stochastic objectives has become a central systems problem in modern artificial intelligence. Adaptive optimization algorithms address the practical difficulty of selecting and maintaining stable step sizes across heterogeneous parameter groups, yet their behavior intersects with training infrastructure, data distribution, model architecture, and deployment governance. This paper provides an interdisciplinary analysis of adaptive optimizers from a systems perspective, emphasizing structural trade-offs rather than isolated convergence proofs. The discussion examines the statistical and geometric properties of non-convex stochastic objectives, the architectural logic of adaptive update rules, and the influence of momentum, second-moment estimation, and decoupled regularization. The paper further investigates distributed training dynamics, including communication bottlenecks, gradient synchronization, and the relationship between batch size, learning rate scaling, and generalization. Attention is given to robustness, fairness, safety, and accountability, since optimization choices shape model behavior in subtle but consequential ways. The analysis extends to sustainability and operational policy, considering energy consumption, carbon reporting, and the governance of large-scale training runs. It argues that adaptive optimization should be treated as a sociotechnical infrastructure concern, in which algorithmic design, system architecture, evaluation practice, and institutional oversight are co-constituted. The paper concludes with forward-looking perspectives on adaptive methods that are more transparent, resource-aware, and aligned with broader societal expectations for trustworthy machine learning systems.
References
1. Kingma, D. P., & Ba, J. (2015). Adam: A method for stochastic optimization. In 3rd International Conference on Learning Representations. arXiv preprint arXiv:1412.6980.
2. Duchi, J., Hazan, E., & Singer, Y. (2011). Adaptive subgradient methods for online learning and stochastic optimization. Journal of Machine Learning Research, 12, 2121–2159.
3. 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.
4. Reddi, S. J., Kale, S., & Kumar, S. (2018). On the convergence of Adam and beyond. In International Conference on Learning Representations.
5. Loshchilov, I., & Hutter, F. (2019). Decoupled weight decay regularization. In International Conference on Learning Representations.
6. Goyal, P., Dollár, P., Girshick, R., Noordhuis, P., Wesolowski, L., Kyrola, A., Tulloch, A., Jia, Y., & He, K. (2017). Accurate, large minibatch SGD: Training ImageNet in 1 hour. arXiv preprint arXiv:1706.02677.
7. He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep residual learning for image recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (pp. 770–778).
8. Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, Ł., & Polosukhin, I. (2017). Attention is all you need. In Advances in Neural Information Processing Systems (pp. 5998–6008).
9. Devlin, J., Chang, M.-W., Lee, K., & Toutanova, K. (2019). BERT: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (pp. 4171–4186).
10. Brown, T. B., Mann, B., Ryder, N., Subbiah, M., Kaplan, J., Dhariwal, P., ... Amodei, D. (2020). Language models are few-shot learners. In Advances in Neural Information Processing Systems (pp. 1877–1901).
11. Keskar, N. S., Mudigere, D., Nocedal, J., Smelyanskiy, M., & Tang, P. T. P. (2017). On large-batch training for deep learning: Generalization gap and sharp minima. In International Conference on Learning Representations.
12. Chaudhari, P., Choromanska, A., Soatto, S., LeCun, Y., Baldassi, C., Borgs, C., Chayes, J., Sagun, L., & Zecchina, R. (2019). Entropy-SGD: Biasing gradient descent into wide valleys. Journal of Statistical Mechanics: Theory and Experiment, 2019(12), 124018.
13. Frankle, J., & Carbin, M. (2019). The lottery ticket hypothesis: Finding sparse, trainable neural networks. In International Conference on Learning Representations.
14. Jin, R., Cheng, D., Qiao, H., Shi, X., Liu, S., & Zhang, B. (2025). Stochastic gradient descent in non-convex problems: Asymptotic convergence with relaxed step-size via stopping time methods. arXiv preprint arXiv:2504.12601.
15. Amodei, D., Olah, C., Steinhardt, J., Christiano, P., Schulman, J., & Mané, D. (2016). Concrete problems in AI safety. arXiv preprint arXiv:1606.06565.
16. Mitchell, M., Wu, S., Zaldivar, A., Barnes, P., Vasserman, L., Hutchinson, B., Spitzer, E., Raji, I. D., & Gebru, T. (2019). Model cards for model reporting. In Proceedings of the Conference on Fairness, Accountability, and Transparency (pp. 220–229).
17. Strubell, E., Ganesh, A., & McCallum, A. (2019). Energy and policy considerations for deep learning in NLP. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics (pp. 3645–3650).
18. Dean, J., Corrado, G., Monga, R., Chen, K., Devin, M., Mao, M., Ranzato, M., Senior, A., Tucker, P., Yang, K., Le, Q. V., & Ng, A. Y. (2012). Large scale distributed deep networks. In Advances in Neural Information Processing Systems (pp. 1223–1231).
19. Li, M., Andersen, D. G., Park, J. W., Smola, A. J., Ahmed, A., Josifovski, V., Long, J., Shekita, E. J., & Su, B.-Y. (2014). Scaling distributed machine learning with the parameter server. In 11th USENIX Symposium on Operating Systems Design and Implementation (pp. 583–598).
20. Recht, B., Roelofs, R., Schmidt, L., & Shankar, V. (2019). Do ImageNet classifiers generalize to ImageNet? In Proceedings of the 36th International Conference on Machine Learning (pp. 5389–5400).
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