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Improved variance reduction extragradient method with line search for stochastic variational inequalities

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Abstract

In this paper, we investigate the numerical methods for solving stochastic variational inequalities. Using line search scheme, we propose an improved variance based stochastic extragradient method with different step sizes in the prediction and correction steps. The range of correction step size which can guarantee the convergence is also given. For the initial line search step size of each iteration, an adaptive method is adopted. Rather than the same scale for each reduction, a proportional reduction related to the problem is used to meet the line search criteria. Under the assumptions of Lipschitz continuous, pseudo-monotone operator and independent identically distributed sampling, the iterative complexity and the oracle complexity are obtained. When estimating the upper bound of the second order moment of the martingale difference sequence, we give a more convenient and comprehensible proof instead of using the Burkholder-Davis-Gundy inequality. The proposed algorithm is applied to fractional programming problems and the \(l_2\) regularized logistic regression problem. The numerical results demonstrate its superiority.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (Grant Nos. 11871279, 12131004 and 11571178).

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Authors and Affiliations

  1. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, People’s Republic of China

    Ting Li, Xingju Cai, Yongzhong Song & Yumin Ma

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  1. Ting Li
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  2. Xingju Cai
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  4. Yumin Ma
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Correspondence to Yumin Ma.

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Li, T., Cai, X., Song, Y. et al. Improved variance reduction extragradient method with line search for stochastic variational inequalities. J Glob Optim 87, 423–446 (2023). https://doi.org/10.1007/s10898-022-01135-1

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