Marina Danilova and Eduard Gorbunov. Distributed methods with absolute compression and error compensation. In *Mathematical Optimization Theory and Operations Research: Recent Trends: 21st International Conference, MOTOR* 2022, Petrozavodsk, Russia, July 2-6, 2022, Revised Selected Papers, pages 163-177. Springer, 2022.
Alexandre d'Aspremont. Smooth optimization with approximate gradient. SIAM Journal on Optimization, 19(3):1171-1183, 2008.
Olivier Devolder, François Glineur, and Yuri Nesterov. First-order methods of smooth convex optimization with inexact oracle. Mathematical Programming, 146(1-2):37-75, 2014.
Aritra Dutta, El Houcine Bergou, Ahmed M Abdelmoniem, Chen-Yu Ho, Atal Narayan Sahu, Marco Canini, and Panos Kalnis. On the discrepancy between the theoretical analysis and practical implementations of compressed communication for distributed deep learning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 3817-3824, 2020.
Ilyas Fatkhullin, Igor Sokolov, Eduard Gorbunov, Zhize Li, and Peter Richtárik. EF21 with bells & whistles: practical algorithmic extensions of modern error feedback. arXiv preprint arXiv:2110.03294, 2021.
Ian Goodfellow, Yoshua Bengio, and Aaron Courville. Deep Learning. The MIT Press, 2016.
Eduard Gorbunov, Dmitry Kovalev, Dmitry Makarenko, and Peter Richtárik. Linearly converging error compensated SGD. Advances in Neural Information Processing Systems, 33:20889-20900, 2020.
Robert Mansel Gower, Nicolas Loizou, Xun Qian, Alibek Sailanbayev, Egor Shulgin, and Peter Richtárik. SGD: General analysis and improved rates. In International Conference on Machine Learning (ICML), pages 5200-5209. PMLR, 2019.
Suyog Gupta, Ankur Agrawal, Kailash Gopalakrishnan, and Pritish Narayanan. Deep learning with limited numerical precision. In International conference on machine learning, pages 1737-1746. PMLR, 2015.
Samuel Horváth, Chen-Yu Ho, Ludovit Horváth, Atal Narayan Sahu, Marco Canini, and Peter Richtárik. Natural compression for distributed deep learning. In *Mathematical and Scientific Machine Learning*, pages 129–141. PMLR, 2022.
Bin Hu, Peter Seiler, and Laurent Lessard. Analysis of biased stochastic gradient descent using sequential semidefinite programs. Mathematical Programming, 187:383-408, 2021a.
Yifan Hu, Xin Chen, and Niao He. Sample complexity of sample average approximation for conditional stochastic. SIAM J. on Optimization, 30(3):2103-2133, 2020a. ISSN 1052-6234. doi: 10.1137/19M1284865. URL https://doi.org/10.1137/19M1284865.
Yifan Hu, Siqi Zhang, Xin Chen, and Niao He. Biased stochastic first-order methods for conditional stochastic optimization and applications in meta learning. In H. Larochelle, M. Ranzato, R. Hadsell, M.F. Balcan, and H. Lin, editors, Advances in Neural Information Processing Systems, volume 33, pages 2759-2770. Curran Associates, Inc., 2020b. URL https://proceedings.neurips.cc/paper_files/paper/2020/file/1cdf14d1e3699d61d237cf76ce1c2dca-[]Paper.pdf.
Yifan Hu, Xin Chen, and Niao He. On the bias-variance-cost tradeoff of stochastic optimization. In M. Ranzato, A. Beygelzimer, Y. Dauphin, P.S. Liang, and J. Wortman Vaughan, editors, Advances in Neural Information Processing Systems, volume 34, pages 22119-22131. Curran Associates, Inc., 2021b. URL https://proceedings.neurips.cc/paper_files/paper/2021/file/b986700c627db479a4d9460b75de7222-[]Paper.pdf.
Kaiyi Ji, Junjie Yang, and Yingbin Liang. Theoretical convergence of multi-step model-agnostic meta-learning. 23(1), 2022. ISSN 1532-4435.
Hamed Karimi, Julie Nutini, and Mark Schmidt. Linear convergence of gradient and proximal-gradient methods under the Polyak-Łojasiewicz condition. Machine Learning and Knowledge Discovery in Databases, pages 795--811, 2016.