[36] Konstantinos Nikolakakis, Farzin Haddadpour, Dionysis Kalogerias, and Amin Karbasi. Blackbox generalization: Stability of zeroth-order learning. In Advances in Neural Information Processing Systems (NeurIPS), volume 35, pages 31525-31541, 2022.
[37] Moritz Hardt, Ben Recht, and Yoram Singer. Train faster, generalize better: Stability of stochastic gradient descent. In International Conference on Machine Learning (ICML), volume 48, pages 1225-1234, 2016.
[38] Yi Zhou, Yingbin Liang, and Huishuai Zhang. Understanding generalization error of SGD in nonconvex optimization. Machine Learning, 111(1):345-375, 2022.
[39] Wei Shen, Zhenhuan Yang, Yiming Ying, and Xiaoming Yuan. Stability and optimization error of stochastic gradient descent for pairwise learning, 2019.
[40] Yunwen Lei, Mingrui Liu, and Yiming Ying. Generalization guarantee of SGD for pairwise learning. In Advances in Neural Information Processing Systems (NeurIPS), pages 21216-21228, 2021.
[41] Mariia Vladimirova, Stéphane Girard, Hien Nguyen, and Julyan Arbel. Sub-Weibull distributions: Generalizing sub-Gaussian and sub-Exponential properties to heavier-tailed distributions. Stat, 9(1):e318:1–8, 2020.
[42] Arun Kumar Kuchibhotla and Abhishek Chakraborty. Moving beyond sub-Gaussianity in high-dimensional statistics: Applications in covariance estimation and linear regression. Information and Inference: A Journal of the IMA, 11(4):1389-1456, 06 2022.
[43] Mariia Vladimirova, Jakob Verbeek, Pablo Mesejo, and Julyan Arbel. Understanding priors in bayesian neural networks at the unit level. In Kamalika Chaudhuri and Ruslan Salakhutdinov, editors, Proceedings of the 36th International Conference on Machine Learning (ICML), volume 97, pages 6458-6467, 2019.
[44] Shaojie Li and Yong Liu. High probability guarantees for nonconvex stochastic gradient descent with heavy tails. In International Conference on Machine Learning (ICML), volume 162, pages 12931-12963, 2022.
[45] Liam Madden, Emiliano Dall'Anese, and Stephen Becker. High-probability convergence bounds for non-convex stochastic gradient descent, 2020.
[46] Hamed Karimi, Julie Nutini, and Mark Schmidt. Linear convergence of gradient and proximal-gradient methods under the polyak-lojasiewicz condition. In European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML-PKDD), volume 9851, pages 795–811, 2016.
[47] Xiaoge Deng, Tao Sun, Shengwei Li, and Dongsheng Li. Stability-based generalization analysis of the asynchronous decentralized SGD. In the Thirty-Eighth AAAI Conference on Artificial Intelligence (AAAI), pages 7340-7348, 2023.
[48] Xiangru Lian, Wei Zhang, Ce Zhang, and Ji Liu. Asynchronous decentralized parallel stochastic gradient descent. In Proceedings of the 35th International Conference on Machine Learning (ICML), volume 80, pages 3049-3058, 2018.
[49] Ege C. Kaya, Mehmet Berk Sahin, and Abolfazl Hashemi. Communication-efficient zeroth-order distributed online optimization: Algorithm, theory, and applications. IEEE Access, 11:61173-61191, 2023.
[50] Yunwen Lei and Yiming Ying. Sharper generalization bounds for learning with gradient-dominated objective functions. In International Conference on Learning Representations (ICLR), pages 1-23, 2021.
[51] Yunwen Lei, Antoine Ledent, and Marius Kloft. Sharper generalization bounds for pairwise learning. In Advances in Neural Information Processing Systems (NeurIPS), pages 21236-21246, 2020.
[52] Zhenhuan Yang, Yunwen Lei, Puyu Wang, Tianbao Yang, and Yiming Ying. Simple stochastic and online gradient descent algorithms for pairwise learning. In Advances in Neural Information Processing Systems (NeurIPS), pages 20160-20171, 2021.