论文标题
基于方差的Bregman外部算法，并搜索解决随机变化不平等的线路搜索
Variance-Based Bregman Extragradient Algorithm with Line Search for Solving Stochastic Variational Inequalities
论文作者
论文摘要
本文的主要目的是提出一种基于方差的Bregman外部算法，并通过搜索解决随机变化不等式的线路，这与未知的Lipschitz常数相当可靠。我们通过更简洁有效的方法证明了算法几乎可以确定的收敛，而不是使用SuperMartingale Contresgence定理。此外，当$ x $有限时，我们不仅获得了差距函数的收敛速率$ \ mathcal {o}（1/k）$，而且当$ x $不绑定时，自然剩余功能也相同的收敛速率。在薄荷变化不等式条件下，我们得出了迭代复杂度$ \ MATHCAL {O}（1/\ VAREPSILON）$和ORACLE COMPLECTITY $ \ MATHCAL {O}（1/\ VAREPSILON^2）$在两种情况下。最后，一些数值结果证明了所提出的算法的优越性。
The main purpose of this paper is to propose a variance-based Bregman extragradient algorithm with line search for solving stochastic variational inequalities, which is robust with respect an unknown Lipschitz constant. We prove the almost sure convergence of the algorithm by a more concise and effective method instead of using the supermartingale convergence theorem. Furthermore, we obtain not only the convergence rate $\mathcal{O}(1/k)$ with the gap function when $X$ is bounded, but also the same convergence rate in terms of the natural residual function when $X$ is unbounded. Under the Minty variational inequality condition, we derive the iteration complexity $\mathcal{O}(1/\varepsilon)$ and the oracle complexity $\mathcal{O}(1/\varepsilon^2)$ in both cases. Finally, some numerical results demonstrate the superiority of the proposed algorithm.
