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Structured Prediction via the Extragradient Method
2005
Neural Information Processing Systems
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We formulate the estimation problem as a convex-concave saddle-point problem and apply the extragradient method, yielding an algorithm with linear convergence using simple gradient and projection calculations ...
We present experiments on two very different structured prediction tasks: 3D image segmentation and word alignment, illustrating the favorable scaling properties of our algorithm. ...
This work was funded by the DARPA CALO project (03-000219) and Microsoft Research MICRO award (05-081). SLJ was also supported by an NSERC graduate sholarship. ...
dblp:conf/nips/TaskarLJ05
fatcat:hlvszmtsrfeg5pmwlhqk5wvr24
Large-margin structural prediction via linear programming
2009
European Association for Machine Translation Conferences/Workshops
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May 13, 2009 L 1 -Regularized Structured Prediction Z. Wang, J. Shawe-Taylor, S. Szedmák, 10/29 Extragradient Method (Cont.) ...
May 13, 2009 L 1 -Regularized Structured Prediction Z. Wang, J. Shawe-Taylor, S. Szedmák, 13/29 Extragradient Method for LP (Cont.) ...
Suppose w parameterizes the supporting hyperplane for the data set S. ...
dblp:conf/eamt/WangSS09
fatcat:tw6eruptbje4blewfihd57kece
Large-Margin Structured Prediction via Linear Programming
2009
Journal of machine learning research
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The proposed method has the advantages that it can handle arbitrary structures and larger-scale problems. ...
In addition, we also explore the integration of column generation and an extragradient method for linear programming to gain further efficiency. ...
We thank Sándor Szedmák for numerous useful discussions on the extragradient method and providing an initial MATLAB implementation of the original algorithm. ...
dblp:journals/jmlr/WangS09
fatcat:2piy5fengzeqbgn33jzfilyyfi
Relative Lipschitzness in Extragradient Methods and a Direct Recipe for Acceleration
[article]
2021
arXiv
pre-print
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To obtain this result we provide a fine-grained characterization of the convergence rates of extragradient methods for solving monotone variational inequalities in terms of a natural condition we call ...
We show that standard extragradient methods (i.e. mirror prox and dual extrapolation) recover optimal accelerated rates for first-order minimization of smooth convex functions. ...
Acknowledgments The existence of an extragradient algorithm in the primal-dual formulation of smooth minimization directly achieving accelerated rates is due to discussions with the first author, Michael ...
arXiv:2011.06572v2
fatcat:ycwuvjf7gnai3fbt4y44ubv234
Distributed Saddle-Point Problems Under Data Similarity
2021
Neural Information Processing Systems
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We study solution methods for (strongly-)convex-(strongly)-concave Saddle-Point Problems (SPPs) over networks of two type-master/workers (thus centralized) architectures and mesh (thus decentralized) networks ...
strong convexity constant, and is the diameter of the network. ...
Figure 4 compares Algorithm 2 with Decentralized Extragradient method (EGD) [5] and Extragradient method with gradient-tracking (EGD-GT) [27] . ...
dblp:conf/nips/BeznosikovSRG21
fatcat:3doipurcubaafbysggzcpli6mm
Ultra-Low-Complexity Algorithms with Structurally Optimal Multi-Group Multicast Beamforming in Large-Scale Systems
[article]
2022
arXiv
pre-print
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The second algorithm adopts the alternating direction method of multipliers (ADMM) method by converting each SCA subproblem into a favorable ADMM structure. ...
The first algorithm uses a saddle point reformulation in the dual domain and applies the extragradient method with an adaptive step-size procedure to find the saddle point with simple closed-form updates ...
We now show that the prediction-correction procedure guarantees the extragradient algorithm converges to the saddle point u o of problem (8) . ...
arXiv:2206.01846v1
fatcat:h5owmfl2nbcyzjupflejncfngy
Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods
[article]
2023
arXiv
pre-print
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Underlying our algorithm designs are two key elements: (a) converting the original problem into a bilinear minimax problem over probability distributions; (b) exploiting the extragradient idea – in conjunction ...
This paper develops a scalable first-order optimization-based method that computes optimal transport to within ε additive accuracy with runtime O( n^2/ε), where n denotes the dimension of the probability ...
This special structure motivates one to alternate between row and column rescaling until convergence, the key idea behind the Sinkhorn algorithm. Extragradient methods. ...
arXiv:2301.13006v1
fatcat:yrtcm4rb7vaqrbs2nzcnbc2cdi
Minimax in Geodesic Metric Spaces: Sion's Theorem and Algorithms
[article]
2022
arXiv
pre-print
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In our second main result, we specialize to geodesically complete Riemannian manifolds: we devise and analyze the complexity of first-order methods for smooth minimax problems. ...
The first main result of the paper is a geodesic metric space version of Sion's minimax theorem; we believe our proof is novel and transparent, as it relies on Helly's theorem only. ...
Broadly construed, these applications arise via the lens of robust learning with underlying geometric structure (e.g., manifolds). ...
arXiv:2202.06950v1
fatcat:qxyy3xzrt5gthjdg7pr6lvogmm
Single-Call Stochastic Extragradient Methods for Structured Non-monotone Variational Inequalities: Improved Analysis under Weaker Conditions
[article]
2023
arXiv
pre-print
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2023 pre-print arXiv:2302.14043v1 fatcat:yapz7unhrjbkbpgwm6v3ehggt4
Single-call stochastic extragradient methods, like stochastic past extragradient (SPEG) and stochastic optimistic gradient (SOG), have gained a lot of interest in recent years and are one of the most efficient ...
Equipped with this condition, we provide theoretical guarantees for the convergence of single-call extragradient methods for different step-size selections, including constant, decreasing, and step-size-switching ...
On Single-Call Extragradient Methods. The seminal work of Popov [1980] is the first paper that proposes the deterministic Past Extagradient method. ...
arXiv:2302.14043v2
fatcat:lvhyxwrqbbdvbdxux5b67mvdk4
On the Convergence of Stochastic Extragradient for Bilinear Games using Restarted Iteration Averaging
[article]
2022
arXiv
pre-print
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We study the stochastic bilinear minimax optimization problem, presenting an analysis of the same-sample Stochastic ExtraGradient (SEG) method with constant step size, and presenting variations of the ...
In sharp contrasts with the basic SEG method whose last iterate only contracts to a fixed neighborhood of the Nash equilibrium, SEG augmented with iteration averaging provably converges to the Nash equilibrium ...
A key example of such a method is the celebrated extragradient method. ...
arXiv:2107.00464v4
fatcat:dth6pfn4cfadjhpzrrey2vti6m
Fast Policy Extragradient Methods for Competitive Games with Entropy Regularization
[article]
2023
arXiv
pre-print
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Despite recent efforts in understanding the last-iterate convergence of extragradient methods in the unconstrained setting, the theoretical underpinnings of these methods in the constrained settings, especially ...
Motivated by the algorithmic role of entropy regularization in single-agent reinforcement learning and game theory, we develop provably efficient extragradient methods to find the quantal response equilibrium ...
The entropy-regularized value iteration (17) converges at a linear rate, i.e. Approximate value iteration via policy extragradient methods. ...
arXiv:2105.15186v3
fatcat:rywjyhssjjd45nm3znq7aw2zva
Towards Better Understanding of Adaptive Gradient Algorithms in Generative Adversarial Nets
[article]
2020
arXiv
pre-print
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algorithm only requires invoking one stochastic first-order oracle while enjoying state-of-the-art iteration complexity achieved by stochastic extragradient method by . ...
While adaptive gradient methods theory is well understood for minimization problems, the underlying factors driving their empirical success in min-max problems such as GANs remain unclear. ...
ACKNOWLEDGMENTS The authors thank the anonymous reviewers for their helpful comments. M. Liu and T. Yang are partially supported by National Science Foundation CAREER Award 1844403. M. ...
arXiv:1912.11940v2
fatcat:dttxn2qxqrdurpxrxh6vbd3h7i
Distributed Saddle-Point Problems Under Similarity
[article]
2022
arXiv
pre-print
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We study solution methods for (strongly-)convex-(strongly)-concave Saddle-Point Problems (SPPs) over networks of two type - master/workers (thus centralized) architectures and meshed (thus decentralized ...
their strong convexity constant, and Δ is the diameter of the network. ...
The proof is completed by choosing γ according to (19) . Corollary 3 Let we solve the subproblem (10) via Extragradient method with starting point z k and T = O (1 + γL) log 1 ẽ (22) iterations. ...
arXiv:2107.10706v3
fatcat:oei5dqx2jvd6jlx5zrkshws7ae
Fast Saddle-Point Algorithm for Generalized Dantzig Selector and FDR Control with the Ordered l1-Norm
[article]
2016
arXiv
pre-print
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Algorithm performance is compared between ours and other alternatives, including the linearized ADMM, Nesterov's smoothing, Nemirovski's mirror-prox, and the accelerated hybrid proximal extragradient techniques ...
In this paper we propose a primal-dual proximal extragradient algorithm to solve the generalized Dantzig selector (GDS) estimation problem, based on a new convex-concave saddle-point (SP) reformulation ...
Structured prediction, dual extragradient and bregman projections. Journal of Machine Learning Research, 7:1627-1653, 2006. P. Tseng. ...
arXiv:1511.05864v3
fatcat:affcscjs2rf2himp72ztzzgnau
Explore Aggressively, Update Conservatively: Stochastic Extragradient Methods with Variable Stepsize Scaling
[article]
2020
arXiv
pre-print
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Owing to their stability and convergence speed, extragradient methods have become a staple for solving large-scale saddle-point problems in machine learning. ...
The basic premise of these algorithms is the use of an extrapolation step before performing an update; thanks to this exploration step, extra-gradient methods overcome many of the non-convergence issues ...
The extragradient method and its limitations As discussed earlier, the go-to method for saddle-point problems and variational inequalities is the extragradient (EG) algorithm of Korpelevich [16] and its ...
arXiv:2003.10162v2
fatcat:efpokp6m5fcgpmfa25qw6jsnjy
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