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New First-Order Algorithms for Stochastic Variational Inequalities

In this paper, we propose two new solution schemes to solve the stochastic strongly monotone variational inequality (VI) 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 a 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
to reach an -solution for a strongly monotone VI problem with condition number . As a specific application to stochastic VI, we demonstrate how to incorporate a zeroth-order approach for solving stochastic minimax saddle-point problems in our schemes, where only noisy and biased samples of the objective can be obtained, with a total sample complexity of
.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.32 No.4 October-December 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 2745-2772

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

VARIATIONAL INEQUALITY
MINIMAX SADDLE-POINT
STOCHASTIC FIRST-ORDER METHOD
ZEROTH ORDER METHOD

Info Detail Spesifik

https://doi.org/10.1137/21M1441778

Pernyataan Tanggungjawab

Kevin Huang, Shuzhong Zhang

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