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Recent applications that arise in machine learning have surged significant interest in solving min-max saddle point games.
On a theorem of danskin with an application to a theorem of von neumann-sion
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Nonlinear programming
D. P. Bertsekas · 1999
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Degenerate nonlinear programming with a quadratic growth condition
M. Anitescu · 2000
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Trust region methods
A. R. Conn, N. I. Gould, and P. L. Toint · 2000
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Prox-method with rate of convergence 𝒪 ( 1 / t ) \mathcal{O}(1/t) for variational inequalities with lipschitz continuous monotone operators and smooth convex-concave saddle point problems
A. Nemirovski · 2004
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Finite-dimensional variational inequalities and complementarity problems
F. Facchinei and J.-S. Pang · 2007
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Dual extrapolation and its applications to solving variational inequalities and related problems
Y. Nesterov · 2007
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A fast iterative shrinkage-thresholding algorithm for linear inverse problems
A. Beck and M. Teboulle · 2009
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On the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean
R. D. Monteiro and B. F. Svaiter · 2010
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Nonconvex games with side constraints
J.-S. Pang and G. Scutari · 2011
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Introductory lectures on convex optimization: A basic course
Y. Nesterov · 2013
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Explaining and harnessing adversarial examples
I. J. Goodfellow, J. Shlens, and C. Szegedy · 2014
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On the convergence properties of non-euclidean extragradient methods for variational inequalities with generalized monotone operators
C. D. Dang and G. Lan · 2015
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Censoring representations with an adversary
H. Edwards and A. Storkey · 2015
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On the ergodic convergence rates of a first-order primal–dual algorithm
A. Chambolle and T. Pock · 2016
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Frank-wolfe algorithms for saddle point problems
G. Gidel, T. Jebara, and S. Lacoste-Julien · 2016
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Deep learning
I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio · 2016
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Generative adversarial imitation learning
J. Ho and S. Ermon · 2016
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Solving variational inequalities with monotone operators on domains given by linear minimization oracles
A. Juditsky and A. Nemirovski · 2016
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Linear convergence of gradient and proximal-gradient methods under the polyak-łojasiewicz condition
H. Karimi, J. Nutini, and M. Schmidt · 2016
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A unified distributed algorithm for non-cooperative games., 2016
J. S. Pang and M. Razaviyayn · 2016
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Lower bounds for finding stationary points i
Y. Carmon, J. C. Duchi, O. Hinder, and A. Sidford · 2017
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C. Daskalakis, A. Ilyas, V. Syrgkanis, and H. Zeng · 2017
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Adversarial machine learning at scale
A. Kurakin, I. Goodfellow, and S. Bengio · 2017
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Solving weakly-convex-weakly-concave saddle-point problems as weakly-monotone variational inequality
Q. Lin, M. Liu, H. Rafique, and T. Yang · 2018
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Learning adversarially fair and transferable representations
D. Madras, E. Creager, T. Pitassi, and R. Zemel · 2018
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Towards deep learning models resistant to adversarial attacks
A. Madry, A. Makelov, L. Schmidt, D. Tsipras, and A. Vladu · 2018
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Cycles in zero-sum differential games and biological diversity
T. Mai, M. Mihail, I. Panageas, W. Ratcliff, V. Vazirani, and P. Yunker · 2018
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Mirror descent in saddle-point problems: Going the extra (gradient) mile
P. Mertikopoulos, H. Zenati, B. Lecouat, C.-S. Foo, V. Chandrasekhar, and G. Piliouras · 2018
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A. Sinha, H. Namkoong, and J. Duchi · 2017
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Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms
H. Xiao, K. Rasul, and R. Vollgraf · 2017
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The mechanics of n-player differentiable games
D. Balduzzi, S. Racaniere, J. Martens, J. Foerster, K. Tuyls, and T. Graepel · 2018
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Kernel exponential family estimation via doubly dual embedding
B. Dai, H. Dai, A. Gretton, L. Song, D. Schuurmans, and N. He · 2018
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Sbeed: Convergent reinforcement learning with nonlinear function approximation
B. Dai, A. Shaw, L. Li, L. Xiao, N. He, Z. Liu, J. Chen, and L. Song · 2018
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Last-iterate convergence: Zero-sum games and constrained min-max optimization
C. Daskalakis and I. Panageas · 2018
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The limit points of (optimistic) gradient descent in min-max optimization
C. Daskalakis and I. Panageas · 2018
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Which training methods for gans do actually converge?
L. Mescheder, A. Geiger, and S. Nowozin · 2018
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Non-convex min-max optimization: Provable algorithms and applications in machine learning
H. Rafique, M. Liu, Q. Lin, and T. Yang · 2018
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On the convergence and robustness of training gans with regularized optimal transport
M. Sanjabi, J. Ba, M. Razaviyayn, and J. D. Lee · 2018
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P. Sattigeri, S. C. Hoffman, V. Chenthamarakshan, and K. R. Varshney · 2018
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A geometric analysis of phase retrieval
J. Sun, Q. Qu, and J. Wright · 2018
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Fairgan: Fairness-aware generative adversarial networks
D. Xu, S. Yuan, L. Zhang, and X. Wu · 2018
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On the global convergence of imitation learning: A case for linear quadratic regulator
Q. Cai, M. Hong, Y. Chen, and Z. Wang · 2019
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Minmax optimization: Stable limit points of gradient descent ascent are locally optimal
C. Jin, P. Netrapalli, and M. I. Jordan · 2019
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Differentiable game mechanics
A. Letcher, D. Balduzzi, S. Racaniere, J. Martens, J. Foerster, K. Tuyls, and T. Graepel · 2019
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Block alternating optimization for non-convex min-max problems: algorithms and applications in signal processing and communications
S. Lu, I. Tsaknakis, and M. Hong · 2019
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S. Lu, I. Tsaknakis, M. Hong, and Y. Chen · 2019
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Agnostic federated learning
M. Mohri, G. Sivek, and A. T. Suresh · 2019
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A. Mokhtari, A. Ozdaglar, and S. Pattathil · 2019
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Theoretically principled trade-off between robustness and accuracy
H. Zhang, Y. Yu, J. Jiao, E. Xing, L. E. Ghaoui, and M. Jordan · 2019
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