Log In Sign Up

Enhanced First and Zeroth Order Variance Reduced Algorithms for Min-Max Optimization

by   Tengyu Xu, et al.

Min-max optimization captures many important machine learning problems such as robust adversarial learning and inverse reinforcement learning, and nonconvex-strongly-concave min-max optimization has been an active line of research. Specifically, a novel variance reduction algorithm SREDA was proposed recently by (Luo et al. 2020) to solve such a problem, and was shown to achieve the optimal complexity dependence on the required accuracy level ϵ. Despite the superior theoretical performance, the convergence guarantee of SREDA requires stringent initialization accuracy and an ϵ-dependent stepsize for controlling the per-iteration progress, so that SREDA can run very slowly in practice. This paper develops a novel analytical framework that guarantees the SREDA's optimal complexity performance for a much enhanced algorithm SREDA-Boost, which has less restrictive initialization requirement and an accuracy-independent (and much bigger) stepsize. Hence, SREDA-Boost runs substantially faster in experiments than SREDA. We further apply SREDA-Boost to propose a zeroth-order variance reduction algorithm named ZO-SREDA-Boost for the scenario that has access only to the information about function values not gradients, and show that ZO-SREDA-Boost outperforms the best known complexity dependence on ϵ. This is the first study that applies the variance reduction technique to zeroth-order algorithm for min-max optimization problems.


page 1

page 2

page 3

page 4


Complexity Lower Bounds for Nonconvex-Strongly-Concave Min-Max Optimization

We provide a first-order oracle complexity lower bound for finding stati...

Fast Distributionally Robust Learning with Variance Reduced Min-Max Optimization

Distributionally robust supervised learning (DRSL) is emerging as a key ...

Convex-Concave Min-Max Stackelberg Games

Min-max optimization problems (i.e., min-max games) have been attracting...

A Single-Loop Smoothed Gradient Descent-Ascent Algorithm for Nonconvex-Concave Min-Max Problems

Nonconvex-concave min-max problem arises in many machine learning applic...

Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimization

The use of min-max optimization in adversarial training of deep neural n...

SpiderBoost: A Class of Faster Variance-reduced Algorithms for Nonconvex Optimization

There has been extensive research on developing stochastic variance redu...

Selection on X_1+X_2+... + X_m with layer-ordered heaps

Selection on X_1+X_2+... + X_m is an important problem with many applica...