Minimax Optimization with Smooth Algorithmic Adversaries

06/02/2021
by   Tanner Fiez, et al.
23

This paper considers minimax optimization min_x max_y f(x, y) in the challenging setting where f can be both nonconvex in x and nonconcave in y. Though such optimization problems arise in many machine learning paradigms including training generative adversarial networks (GANs) and adversarially robust models, many fundamental issues remain in theory, such as the absence of efficiently computable optimality notions, and cyclic or diverging behavior of existing algorithms. Our framework sprouts from the practical consideration that under a computational budget, the max-player can not fully maximize f(x,·) since nonconcave maximization is NP-hard in general. So, we propose a new algorithm for the min-player to play against smooth algorithms deployed by the adversary (i.e., the max-player) instead of against full maximization. Our algorithm is guaranteed to make monotonic progress (thus having no limit cycles), and to find an appropriate "stationary point" in a polynomial number of iterations. Our framework covers practical settings where the smooth algorithms deployed by the adversary are multi-step stochastic gradient ascent, and its accelerated version. We further provide complementing experiments that confirm our theoretical findings and demonstrate the effectiveness of the proposed approach in practice.

READ FULL TEXT
07/02/2019

Efficient Algorithms for Smooth Minimax Optimization

This paper studies first order methods for solving smooth minimax optimi...
11/05/2016

Generative Multi-Adversarial Networks

Generative adversarial networks (GANs) are a framework for producing a g...
11/23/2018

Kernel-Based Training of Generative Networks

Generative adversarial networks (GANs) are designed with the help of min...
06/22/2020

A Provably Convergent and Practical Algorithm for Min-max Optimization with Applications to GANs

We present a new algorithm for optimizing min-max loss functions that ar...
11/01/2016

Computationally Efficient Influence Maximization in Stochastic and Adversarial Models: Algorithms and Analysis

We consider the problem of influence maximization in fixed networks, for...
09/22/2022

Nonsmooth Composite Nonconvex-Concave Minimax Optimization

Nonconvex-concave minimax optimization has received intense interest in ...
06/25/2020

Newton-type Methods for Minimax Optimization

Differential games, in particular two-player sequential games (a.k.a. mi...