Adaptive and Universal Single-gradient Algorithms for Variational Inequalities

10/15/2020
by   Alina Ene, et al.
0

Variational inequalities with monotone operators capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Classical methods based on the MirrorProx algorithm require two operator evaluations per iteration, which is the dominant factor in the running time in many settings. Additionally, the algorithms typically require careful settings of the step sizes based on the parameters of the problems such as smoothness. In this work, we develop new algorithms addressing both of these shortcomings simultaneously. Our algorithms use a single operator evaluation per iteration and automatically adapt to problem parameters such as smoothness. We show that our algorithms are universal and simultaneously achieve the optimal convergence rates in the non-smooth, smooth, and stochastic settings.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/05/2019

A Universal Algorithm for Variational Inequalities Adaptive to Smoothness and Noise

We consider variational inequalities coming from monotone operators, a s...
research
11/23/2020

Geometry-Aware Universal Mirror-Prox

Mirror-prox (MP) is a well-known algorithm to solve variational inequali...
research
07/09/2020

Higher-order methods for convex-concave min-max optimization and monotone variational inequalities

We provide improved convergence rates for constrained convex-concave min...
research
04/10/2023

First-order methods for Stochastic Variational Inequality problems with Function Constraints

The monotone Variational Inequality (VI) is an important problem in mach...
research
02/09/2019

Forward-backward-forward methods with variance reduction for stochastic variational inequalities

We develop a new stochastic algorithm with variance reduction for solvin...
research
02/20/2020

Halpern Iteration for Near-Optimal and Parameter-Free Monotone Inclusion and Strong Solutions to Variational Inequalities

We leverage the connections between nonexpansive maps, monotone Lipschit...
research
04/20/2020

From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds

In this work we study statistical properties of graph-based clustering a...

Please sign up or login with your details

Forgot password? Click here to reset