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Stochastic Variance Reduction for Variational Inequality Methods [article]

Ahmet Alacaoglu, Yura Malitsky
2022 arXiv   pre-print
We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions.  ...  Our results reinforce the correspondence between variance reduction in variational inequalities and minimization.  ...  Our work shows that there is indeed a natural correspondence between variance reduction in variational inequalities and minimization.  ... 
arXiv:2102.08352v2 fatcat:mzekjor7ovahzatb2ft7xdvxhq

Extragradient method with variance reduction for stochastic variational inequalities [article]

Alfredo Iusem, Alejandro Jofré, Roberto I. Oliveira, Philip Thompson
2017 arXiv   pre-print
We propose an extragradient method with stepsizes bounded away from zero for stochastic variational inequalities requiring only pseudo-monotonicity.  ...  Our results provide new classes of stochastic variational inequalities for which a convergence rate of O(1/K) holds in terms of the mean-squared distance to the solution set.  ...  The authors are grateful for the referees' constructive comments.  ... 
arXiv:1703.00260v1 fatcat:ywjlr54mdff5ljw7kzpsdtvvcu

Forward-backward-forward methods with variance reduction for stochastic variational inequalities [article]

Radu Ioan Bot and Panayotis Mertikopoulos and Mathias Staudigl and Phan Tu Vuong
2019 arXiv   pre-print
We develop a new stochastic algorithm with variance reduction for solving pseudo-monotone stochastic variational inequalities.  ...  Our algorithm incorporates a variance reduction mechanism and leads to almost sure (a.s.) convergence to an optimal solution.  ...  variational inequality problem.  ... 
arXiv:1902.03355v1 fatcat:6fe74xsxafb57nngf7yiod74ce

Convergent Noisy forward-backward-forward algorithms in non-monotone variational inequalities

Mathias Staudigl, Panayotis Mertikopoulos
2019 IFAC-PapersOnLine  
We develop a new stochastic algorithm with variance reduction for solving pseudomonotone stochastic variational inequalities.  ...  Abstract: We develop a new stochastic algorithm with variance reduction for solving pseudomonotone stochastic variational inequalities.  ...  Our algorithm incorporates a variance reduction mechanism, and leads to a.s. convergence to solutions of a merely pseudo-monotone stochastic variational inequality problem.  ... 
doi:10.1016/j.ifacol.2019.06.021 fatcat:7o25s26bnjhyhnbqajzpy2qhza

Accelerated variance reduction methods on GPU

Chuan-Hsiang Han, Yu-Tuan Lin
2014 2014 20th IEEE International Conference on Parallel and Distributed Systems (ICPADS)  
We show that the total effect of combining variance reduction methods as efficient software algorithms with GPU acceleration as a parallel-computing hardware device can yield a tremendous speed up for  ...  Variance reduction methods have been developed as efficient algorithms by means of probabilistic analysis. GPU acceleration plays a crucial role of increasing the total number of simulations.  ...  Han thanks a student team from the SCOPE lab from Department of Computer Science, National Tsing-Hua University, for generating numerical results of importance sampling on GPU, and Nvidia-NTHU joint lab  ... 
doi:10.1109/padsw.2014.7097926 dblp:conf/icpads/HanL14 fatcat:ydfqhbo3anfyxbq64fsgyqsfxe

A martingale control variate method for option pricing with stochastic volatility

Jean-Pierre Fouque, Chuan-Hsiang Han
2007 E S A I M: Probability & Statistics  
A generic control variate method is proposed to price options under stochastic volatility models by Monte Carlo simulations.  ...  On the other hand, variance reduction methods seek probabilistic ways to reformulate the pricing problem considered in order to gain significant variance reduction.  ...  Acknowledgment The authors would like to thank Bernard Lapeyre for his helpful comments and suggestions on an earlier version of this work.  ... 
doi:10.1051/ps:2007005 fatcat:smesoxqncrgn3mrtfeagvlwnae

On Multilevel and Control Variate Monte Carlo Methods for Option Pricing under the Rough Heston Model

Siow Woon Jeng, Adem Kiliçman
2021 Mathematics  
The numerical experiments indicate that the proposed method is capable of achieving a substantial cost-adjusted variance reduction up to 17 times, and it is better than its predecessor individual methods  ...  In addition, we propose a mixed Monte Carlo method, using the control variate and multilevel methods.  ...  Control Variate Method The control variate method is one of the variance reduction methods along with antithetic variates, quasi Monte Carlo, and importance sampling methods.  ... 
doi:10.3390/math9222930 fatcat:dev33f2dfrheraiosmywsikfre

A combined deterministic and sampling-based sequential bounding method for stochastic programming

Peguy Pierre-Louis, Guzin Bayraksan, David P. Morton
2011 Proceedings of the 2011 Winter Simulation Conference (WSC)  
An upper bound estimator is formed through a stratified Monte Carlo sampling procedure that includes the use of a control variate variance reduction scheme.  ...  We develop an algorithm for two-stage stochastic programming with a convex second stage program and with uncertainty in the right-hand side.  ...  Variance Reduction We study variance reduction in SSAM for the different estimators we have proposed.  ... 
doi:10.1109/wsc.2011.6148105 dblp:conf/wsc/Pierre-LouisBM11 fatcat:meqmufl3qvgp5cmhbcdmdptizi

Adaptive Monte Carlo Variance Reduction with Two-time-scale Stochastic Approximation

Reiichiro Kawai
2007 Monte Carlo Methods and Applications  
Combined control variates and importance sampling variance reduction and its two-fold optimality are investigated.  ...  Two-time-scale stochastic approximation algorithm is applied in parameter search for the combination and almost sure convergence of the algorithm to the unique optimum is proved.  ...  many problem-specific variance reduction methods in the literature.  ... 
doi:10.1515/mcma.2007.010 fatcat:kqlt4t4hh5e4vhf6upr6z3zgaq

Variance reduction in stochastic methods for large-scale regularised least-squares problems [article]

Yusuf Pilavcı
2021 arXiv   pre-print
We apply this technique to Tikhonov regularization on graphs, where the reduction in variance is found to be substantial at very small extra cost.  ...  We show here that variance can be reduced by combining the stochastic estimator with a deterministic gradient-descent step, while keeping the property of unbiasedness.  ...  (5) : Connection with control variates. The proposed method is a particular instance of the control variate method.  ... 
arXiv:2110.07894v1 fatcat:bfclsyi4dvfhfkchyz2ouk2bly

Demographic Stochasticity and the Variance Reduction Effect

Gordon A. Fox, Bruce E. Kendall
2002 Ecology  
Demographic stochasticity is almost universally modeled as sampling variance in a homogeneous population, although it is defined as arising from random variation among individuals.  ...  (convex or concave) of the mean-variance relationship; and (3) information on the mechanisms generating among-individual variation.  ...  VARIANCE REDUCTION AND RANDOM ASSIGNMENT OF SURVIVAL PROBABILITIES Kendall and Fox (2002) observed that the reduction in demographic stochasticity due to individual variation requires that survival probabilities  ... 
doi:10.2307/3071775 fatcat:2onam6cfzzdzlpxtny2ixrr6xa

DEMOGRAPHIC STOCHASTICITY AND THE VARIANCE REDUCTION EFFECT

Gordon A. Fox, Bruce E. Kendall
2002 Ecology  
Demographic stochasticity is almost universally modeled as sampling variance in a homogeneous population, although it is defined as arising from random variation among individuals.  ...  (convex or concave) of the mean-variance relationship; and (3) information on the mechanisms generating among-individual variation.  ...  VARIANCE REDUCTION AND RANDOM ASSIGNMENT OF SURVIVAL PROBABILITIES Kendall and Fox (2002) observed that the reduction in demographic stochasticity due to individual variation requires that survival probabilities  ... 
doi:10.1890/0012-9658(2002)083[1928:dsatvr]2.0.co;2 fatcat:5u2zn23nqjatjf5x5lx64wowme

Altruism in a volatile world

Patrick Kennedy, Andrew D. Higginson, Andrew N. Radford, Seirian Sumner
2018 Nature  
This theory-known as inclusive fitness-is founded on a simple inequality termed Hamilton's rule.  ...  For half a century, attempts to understand altruism have developed around the concept that altruists may help relatives to have extra offspring in order to spread shared genes.  ...  Acknowledgements We thank Andy Gardner for helpful discussions in the early stages of this work, and PK thanks the Behaviour Discussion Group at the Smithsonian Tropical Research Institute in Panama for  ... 
doi:10.1038/nature25965 pmid:29513655 pmcid:PMC5986084 fatcat:3u4o3pma2veeppk6jzc5kg6hjy

Nearly Optimal Linear Convergence of Stochastic Primal-Dual Methods for Linear Programming [article]

Haihao Lu, Jinwen Yang
2021 arXiv   pre-print
In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP.  ...  We show that the proposed stochastic method exhibits a linear convergence rate for solving sharp instances with a high probability.  ...  More recently, [2] proposes a stochastic extragradient method with variance reduction for solving variational inequalities.  ... 
arXiv:2111.05530v2 fatcat:ai72hb6lsngp5drit2ecegreya

Accelerating Minibatch Stochastic Gradient Descent using Stratified Sampling [article]

Peilin Zhao, Tong Zhang
2014 arXiv   pre-print
Stochastic Gradient Descent (SGD) is a popular optimization method which has been applied to many important machine learning tasks such as Support Vector Machines and Deep Neural Networks.  ...  Encouraging experimental results confirm the effectiveness of the proposed method.  ...  This paper considers a different variance reduction method using stratified sampling for minibatch SGD training.  ... 
arXiv:1405.3080v1 fatcat:qem2auyfqzfeldhwq7wuak2tn4
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