[36] Jiaming Liang and Yongxin Chen. A proximal algorithm for sampling from non-smooth potentials. In 2022 Winter Simulation Conference (WSC), pages 3229-3240. IEEE, 2022.
[37] Songtao Lu, Meisam Razaviyayn, Bo Yang, Kejun Huang, and Mingyi Hong. Finding second-order stationary points efficiently in smooth nonconvex linearly constrained optimization problems. Advances in Neural Information Processing Systems, 33:2811-2822, 2020.
[38] Frank McSherry and Kunal Talwar. Mechanism design via differential privacy. In 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07), pages 94-103. IEEE, 2007.
[39] Kentaro Minami, HItomi Arai, Issei Sato, and Hiroshi Nakagawa. Differential privacy without sensitivity. Advances in Neural Information Processing Systems, 29, 2016.
[40] Felix Otto and Cédric Villani. Generalization of an inequality by talagrand and links with the logarithmic sobolev inequality. Journal of Functional Analysis, 173(2):361-400, 2000.
[41] Shuang Song, Kamalika Chaudhuri, and Anand D Sarwate. Stochastic gradient descent with differentially private updates. In 2013 IEEE Global Conference on Signal and Information Processing, pages 245-248. IEEE, 2013.
[42] Shuang Song, Thomas Steinke, Om Thakkar, and Abhradeep Thakurta. Evading the curse of dimensionality in unconstrained private glms. In International Conference on Artificial Intelligence and Statistics, pages 2638-2646. PMLR, 2021.
[43] Kunal Talwar, Abhradeep Guha Thakurta, and Li Zhang. Nearly optimal private lasso. Advances in Neural Information Processing Systems, 28, 2015.
[44] Hoang Tran and Ashok Cutkosky. Momentum aggregation for private non-convex erm. In Advances in Neural Information Processing Systems, 2022.
[45] Joel A Tropp. An introduction to matrix concentration inequalities. Foundations and Trends® in Machine Learning, 8(1-2):1-230, 2015.
[46] Di Wang, Changyou Chen, and Jinhui Xu. Differentially private empirical risk minimization with non-convex loss functions. In International Conference on Machine Learning, pages 6526–6535. PMLR, 2019.
[47] Di Wang and Jinhui Xu. Differentially private empirical risk minimization with smooth nonconvex loss functions: A non-stationary view. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, pages 1182-1189, 2019.
[48] Di Wang and Jinhui Xu. Escaping saddle points of empirical risk privately and scalably via dp-trust region method. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases, pages 90-106. Springer, 2020.
[49] Di Wang, Minwei Ye, and Jinhui Xu. Differentially private empirical risk minimization revisited: Faster and more general. Advances in Neural Information Processing Systems, 30, 2017.
[50] Lingxiao Wang, Bargav Jayaraman, David Evans, and Quanquan Gu. Efficient privacy-preserving stochastic nonconvex optimization. arXiv preprint arXiv:1910.13659, 2019.
[51] Yongqiang Wang and Tamer Başar. Decentralized nonconvex optimization with guaranteed privacy and accuracy. Automatica, 150:110858, 2023.
[52] Zhe Wang, Kaiyi Ji, Yi Zhou, Yingbin Liang, and Vahid Tarokh. Spiderboost and momentum: Faster variance reduction algorithms. Advances in Neural Information Processing Systems, 32, 2019.
[53] Yi Xu, Rong Jin, and Tianbao Yang. First-order stochastic algorithms for escaping from saddle points in almost linear time. Advances in neural information processing systems, 31, 2018.
[54] Xiaodong Yang, Huishuai Zhang, Wei Chen, and Tie-Yan Liu. Normalized/clipped sgd with perturbation for differentially private non-convex optimization. arXiv preprint arXiv:2206.13033, 2022.