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In this paper, we propose two new solution schemes to solve the stochastic strongly monotone variational inequality problems: the stochastic extra-point solution scheme and the stochastic extra-momentum solution scheme. The first one is a general scheme based on updating the iterative sequence and an auxiliary extra-point sequence. In the case of deterministic VI model, this approach includes several state-of-the-art first-order methods as its special cases. The second scheme combines two momentum-based directions: the so-called heavy-ball direction and the optimism direction, where only one projection per iteration is required in its updating process. We show that, if the variance of the stochastic oracle is appropriately controlled, then both schemes can be made to achieve optimal iteration complexity of $mathcal{O}left(kappalnleft(frac{1}{epsilon}right)right)$ to reach an $epsilon$-solution for a strongly monotone VI problem with condition number $kappa$. We show that these methods can be readily incorporated in a zeroth-order approach to solve stochastic minimax saddle-point problems, where only noisy and biased samples of the objective can be obtained, with a total sample complexity of $mathcal{O}left(frac{kappa^2}{epsilon}lnleft(frac{1}{epsilon}right)right)$
In this paper, we propose a unifying framework incorporating several momentum-related search directions for solving strongly monotone variational inequalities. The specific combinations of the search directions in the framework are made to guarantee
In this paper, we consider a stochastic distributed nonconvex optimization problem with the cost function being distributed over $n$ agents having access only to zeroth-order (ZO) information of the cost. This problem has various machine learning app
We develop new perturbation techniques for conducting convergence analysis of various first-order algorithms for a class of nonsmooth optimization problems. We consider the iteration scheme of an algorithm to construct a perturbed stationary point se
We present Free-MESSAGEp, the first zeroth-order algorithm for convex mean-semideviation-based risk-aware learning, which is also the first three-level zeroth-order compositional stochastic optimization algorithm, whatsoever. Using a non-trivial exte
In this paper, we consider two formulations for Linear Matrix Inequalities (LMIs) under Slater type constraint qualification assumption, namely, SDP smooth and non-smooth formulations. We also propose two first-order linearly convergent algorithms fo