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In the paper, we propose a class of accelerated zeroth-order and first-order momentum methods for both nonconvex mini-optimization and minimax-optimization.
Nonconvex zeroth-order stochastic admm methods with lower function query complexity
Feihu Huang, Shangqian Gao, Jian Pei, and Heng Huang · 1907
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Min-max optimization without gradients: Convergence and applications to adversarial ml
Sijia Liu, Songtao Lu, Xiangyi Chen, Yao Feng, Kaidi Xu, Abdullah Al-Dujaili, Minyi Hong, and Una-May Obelilly · 1909
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Towards better understanding of adaptive gradient algorithms in generative adversarial nets
Mingrui Liu, Youssef Mroueh, Jerret Ross, Wei Zhang, Xiaodong Cui, Payel Das, and Tianbao Yang · 1912
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Ssvm: A smooth support vector machine for classification
Yuh-Jye Lee and Olvi L Mangasarian · 2001
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Minimax analysis of stochastic problems
Alexander Shapiro and Anton Kleywegt · 2002
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Enhanced first and zeroth order variance reduced algorithms for min-max optimization
Tengyu Xu, Zhe Wang, Yingbin Liang, and H Vincent Poor · 2006
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Zi Xu, Huiling Zhang, Yang Xu, and Guanghui Lan · 2006
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Stochastic first-and zeroth-order methods for nonconvex stochastic programming
Saeed Ghadimi and Guanghui Lan · 2013
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Accelerating stochastic gradient descent using predictive variance reduction
Rie Johnson and Tong Zhang · 2013
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Optimal rates for zero-order convex optimization: The power of two function evaluations
John C Duchi, Michael I Jordan, Martin J Wainwright, and Andre Wibisono · 2015
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Variance reduction for faster non-convex optimization
Zeyuan Allen-Zhu and Elad Hazan · 2016
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Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization
Saeed Ghadimi, Guanghui Lan, and Hongchao Zhang · 2016
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Stochastic variance reduction for nonconvex optimization
Sashank J Reddi, Ahmed Hefny, Suvrit Sra, Barnabas Poczos, and Alex Smola · 2016
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Stochastic online auc maximization
Yiming Ying, Longyin Wen, and Siwei Lyu · 2016
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Random gradient-free minimization of convex functions
Yurii Nesterov and Vladimir G. Spokoiny · 2017
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Zeroth-order (non)-convex stochastic optimization via conditional gradient and gradient updates
Krishnakumar Balasubramanian and Saeed Ghadimi · 2018
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A frank-wolfe framework for efficient and effective adversarial attacks
Jinghui Chen, Dongruo Zhou, Jinfeng Yi, and Quanquan Gu · 2018
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Spider: Near-optimal non-convex optimization via stochastic path-integrated differential estimator
Cong Fang, Chris Junchi Li, Zhouchen Lin, and Tong Zhang · 2018
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On the information-adaptive variants of the admm: an iteration complexity perspective
Xiang Gao, Bo Jiang, and Shuzhong Zhang · 2018
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Zeroth-order stochastic projected gradient descent for nonconvex optimization
Sijia Liu, Xingguo Li, Pin-Yu Chen, Jarvis Haupt, and Lisa Amini · 2018
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Lectures on convex optimization , volume 137
Yurii Nesterov · 2018
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Towards gradient free and projection free stochastic optimization
Anit Kumar Sahu, Manzil Zaheer, and Soummya Kar · 2019
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Efficient algorithms for smooth minimax optimization
Kiran K Thekumparampil, Prateek Jain, Praneeth Netrapalli, and Sewoong Oh · 2019
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A hybrid stochastic optimization framework for stochastic composite nonconvex optimization
Quoc Tran-Dinh, Nhan H Pham, Dzung T Phan, and Lam M Nguyen · 2019
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Variance reduced policy evaluation with smooth function approximation
Hoi-To Wai, Mingyi Hong, Zhuoran Yang, Zhaoran Wang, and Kexin Tang · 2019
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Spiderboost and momentum: Faster variance reduction algorithms
Zhe Wang, Kaiyi Ji, Yi Zhou, Yingbin Liang, and Vahid Tarokh · 2019
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Hassan Rafique, Mingrui Liu, Qihang Lin, and Tianbao Yang · 2018
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Multi-agent reinforcement learning via double averaging primal-dual optimization
Hoi-To Wai, Zhuoran Yang, Zhaoran Wang, and Mingyi Hong · 2018
Cited alongside, same era.
Stochastic nested variance reduction for nonconvex optimization
Dongruo Zhou, Pan Xu, and Quanquan Gu · 2018
Cited alongside, same era.
Lower bounds for non-convex stochastic optimization
Yossi Arjevani, Yair Carmon, John C Duchi, Dylan J Foster, Nathan Srebro, and Blake Woodworth · 2019
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Zo-adamm: Zeroth-order adaptive momentum method for black-box optimization
Xiangyi Chen, Sijia Liu, Kaidi Xu, Xingguo Li, Xue Lin, Mingyi Hong, and David Cox · 2019
Cited alongside, same era.
Momentum-based variance reduction in non-convex sgd
Ashok Cutkosky and Francesco Orabona · 2019
Cited alongside, same era.
Simple black-box adversarial attacks
Chuan Guo, Jacob Gardner, Yurong You, Andrew Gordon Wilson, and Kilian Weinberger · 2019
Cited alongside, same era.
Radu Ioan Boţ and Axel Böhm · 2020
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Zeroth-order deterministic policy gradient
Harshat Kumar, Dionysios S Kalogerias, George J Pappas, and Alejandro Ribeiro · 2020
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Near-optimal algorithms for minimax optimization
Tianyi Lin, Chi Jin, Michael Jordan, et al · 2020
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Luo Luo, Haishan Ye, and Tong Zhang · 2020
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Derivative-free methods for policy optimization: Guarantees for linear quadratic systems
Dhruv Malik, Ashwin Pananjady, Kush Bhatia, Koulik Khamaru, Peter L Bartlett, and Martin J Wainwright · 2020
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Efficient search of first-order nash equilibria in nonconvex-concave smooth min-max problems
Dmitrii M Ostrovskii, Andrew Lowy, and Meisam Razaviyayn · 2020
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A practical online method for distributionally deep robust optimization
Qi Qi, Zhishuai Guo, Yi Xu, Rong Jin, and Tianbao Yang · 2020
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Hybrid variance-reduced sgd algorithms for nonconvex-concave minimax problems
Quoc Tran-Dinh, Deyi Liu, and Lam M Nguyen · 2020
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Zeroth-order algorithms for nonconvex minimax problems with improved complexities
Zhongruo Wang, Krishnakumar Balasubramanian, Shiqian Ma, and Meisam Razaviyayn · 2020
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Sharp analysis of epoch stochastic gradient descent ascent methods for min-max optimization
Yan Yan, Yi Xu, Qihang Lin, Wei Liu, and Tianbao Yang · 2020
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Junchi Yang, Negar Kiyavash, and Niao He · 2020
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A primal dual smoothing framework for max-structured nonconvex optimization
Renbo Zhao · 2020
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