论文标题
加速差异降低了有限和优化的超点方法
An Accelerated Variance Reduced Extra-Point Approach to Finite-Sum VI and Optimization
论文作者
论文摘要
在本文中，我们开发了随机方差降低算法，用于求解一类有限的单调VI，其中操作员由有限的许多单调VI映射和有限的许多单调梯度映射总和组成。当VI映射之和强烈单调或仅单调时，我们研究了在设置下所提出算法的梯度复杂性。此外，我们考虑只有通过嘈杂的随机估计器访问每个VI映射和梯度映射并建立样品梯度复杂性时的情况。我们证明了所提出的算法在使用有限的不等式约束中求解有限的和凸优化的应用，并在仅可用的目标/约束函数值的嘈杂和有偏见的样本时开发Zeroth-rorder方法。
In this paper, we develop stochastic variance reduced algorithms for solving a class of finite-sum monotone VI, where the operator consists of the sum of finitely many monotone VI mappings and the sum of finitely many monotone gradient mappings. We study the gradient complexities of the proposed algorithms under the settings when the sum of VI mappings is either strongly monotone or merely monotone. Furthermore, we consider the case when each of the VI mapping and gradient mapping is only accessible via noisy stochastic estimators and establish the sample gradient complexity. We demonstrate the application of the proposed algorithms for solving finite-sum convex optimization with finite-sum inequality constraints and develop a zeroth-order approach when only noisy and biased samples of objective/constraint function values are available.
