A Variational Inequality Perspective on Generative Adversarial Networks

Abstract

Generative adversarial networks (GANs) form a generative modeling approach known for producing appealing samples, but they are notably difficult to train. One common way to tackle this issue has been to propose new formulations of the GAN objective. Yet, surprisingly few studies have looked at optimization methods designed for this adversarial training. In this work, we cast GAN optimization problems in the general variational inequality framework. Tapping into the mathematical programming literature, we counter some common misconceptions about the difficulties of saddle point optimization and propose to extend techniques designed for variational inequalities to the training of GANs. We apply averaging, extrapolation and a computationally cheaper variant that we call extrapolation from the past to the stochastic gradient method (SGD) and Adam.

Appears in: Proceedings of the Seventh International Conference on Learning Representations (ICLR 2019). Minor modifications with respect to the ICLR version (First paragraph of page 2 and section 3.3): New reference [Popov 1980] and discussion with regards to the novelty of extrapolation from the past. 38 pages

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• A Systematic Survey of Regularization and Normalization in GANs
• Reducing Noise in GAN Training with Variance Reduced Extragradient
• Near-Optimal Algorithms for Minimax Optimization
• Last-iterate convergence rates for min-max optimization
• A Decentralized Parallel Algorithm for Training Generative Adversarial Nets
• Small-GAN: Speeding Up GAN Training Using Core-sets
• Explore Aggressively, Update Conservatively: Stochastic Extragradient Methods with Variable Stepsize Scaling
• Local Saddle Point Optimization: A Curvature Exploitation Approach
• Global Convergence to the Equilibrium of GANs using Variational Inequalities
• On the convergence of single-call stochastic extra-gradient methods
• Painless Stochastic Gradient: Interpolation, Line-Search, and Convergence Rates
• Accelerating Smooth Games by Manipulating Spectral Shapes
• First-order Convergence Theory for Weakly-Convex-Weakly-Concave Min-max Problems
• Towards Better Understanding of Adaptive Gradient Algorithms in Generative Adversarial Nets
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• Stochastic Variance Reduction for Variational Inequality Methods
• Negative Momentum for Improved Game Dynamics
• Improved Algorithms for Convex-Concave Minimax Optimization
• Zeroth-Order Algorithms for Nonconvex Minimax Problems with Improved Complexities
• Finding Mixed Nash Equilibria of Generative Adversarial Networks
• Revisiting Stochastic Extragradient
• A Decentralized Proximal Point-type Method for Saddle Point Problems
• Smooth Monotone Stochastic Variational Inequalities and Saddle Point Problems: A Survey
• Last Iterate is Slower than Averaged Iterate in Smooth Convex-Concave Saddle Point Problems
• Top-k Training of GANs: Improving GAN Performance by Throwing Away Bad Samples
• A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity
• A game-theoretic approach for Generative Adversarial Networks
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• The limits of min-max optimization algorithms: convergence to spurious non-critical sets
• A Unified Analysis of First-Order Methods for Smooth Games via Integral Quadratic Constraints
• Local Stochastic Gradient Descent Ascent: Convergence Analysis and Communication Efficiency
• Adversarial Example Games
• Robust Reinforcement Learning via Adversarial training with Langevin Dynamics
• Complexity Lower Bounds for Nonconvex-Strongly-Concave Min-Max Optimization
• Stochastic Relaxed Inertial Forward-Backward-Forward splitting for Monotone Inclusions in Hilbert spaces
• Linear Last-iterate Convergence in Constrained Saddle-point Optimization
• Accelerated Algorithms for Smooth Convex-Concave Minimax Problems with $\mathcal{O}(1/k^2)$ Rate on Squared Gradient Norm
• Tight last-iterate convergence rates for no-regret learning in multi-player games
• Adaptive Learning in Continuous Games: Optimal Regret Bounds and Convergence to Nash Equilibrium
• A mean-field analysis of two-player zero-sum games
• Generative Minimization Networks: Training GANs Without Competition
• Near-optimal Local Convergence of Alternating Gradient Descent-Ascent for Minimax Optimization
• Train simultaneously, generalize better: Stability of gradient-based minimax learners
• Extragradient Method: $O(1/K)$ Last-Iterate Convergence for Monotone Variational Inequalities and Connections With Cocoercivity
• Taming GANs with Lookahead-Minmax
• A Tight and Unified Analysis of Gradient-Based Methods for a Whole Spectrum of Games
• Influence Estimation for Generative Adversarial Networks
• Halpern Iteration for Near-Optimal and Parameter-Free Monotone Inclusion and Strong Solutions to Variational Inequalities
• An automatic system to detect equivalence between iterative algorithms
• Training Generative Adversarial Networks with Adaptive Composite Gradient
• Near Optimal Stochastic Algorithms for Finite-Sum Unbalanced Convex-Concave Minimax Optimization
• Extragradient with player sampling for faster Nash equilibrium finding
• On the Convergence of (Stochastic) Gradient Descent with Extrapolation for Non-Convex Optimization
• Extrapolation for Large-batch Training in Deep Learning
• Finding Mixed Strategy Nash Equilibrium for Continuous Games through Deep Learning
• Stochastic Extragradient: General Analysis and Improved Rates
• Bayesian Optimization of Sampling Densities in MRI
• A Distributed Training Algorithm of Generative Adversarial Networks with Quantized Gradients
• Bridging Explicit and Implicit Deep Generative Models via Neural Stein Estimators
• Semi-Anchored Multi-Step Gradient Descent Ascent Method for Structured Nonconvex-Nonconcave Composite Minimax Problems
• An Exponentially Converging Particle Method for the Mixed Nash Equilibrium of Continuous Games
• Optimal Analysis of Method with Batching for Monotone Stochastic Finite-Sum Variational Inequalities
• Local AdaGrad-Type Algorithm for Stochastic Convex-Concave Optimization
• Forward Looking Best-Response Multiplicative Weights Update Methods for Bilinear Zero-sum Games
• Convex-Concave Min-Max Stackelberg Games
• Modelling and simulating spatial extremes by combining extreme value theory with generative adversarial networks
• Mirror frameworks for relatively Lipschitz and monotone-like variational inequalities
• Complex Momentum for Optimization in Games