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The complexity of computing a Nash equilibrium
TLDR
We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Expand
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Training GANs with Optimism
TLDR
We address the issue of limit cycling behavior in training Generative Adversarial Networks and propose the use of Optimistic Mirror Decent (OMD) for Wasserstein GANs. Expand
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The Complexity of Computing a Nash Equilibrium
TLDR
We show that finding a Nash equilibrium in three-player games is indeed PPAD-complete; and we do so by a reduction from Brouwer's problem, thus establishing that the two problems are computationally equivalent. Expand
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Optimal Testing for Properties of Distributions
TLDR
We provide a general approach via which we obtain sample-optimal and computationally efficient testers for all these distribution families. Expand
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The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization
TLDR
We characterize the limit points of two basic first order methods, namely Gradient Descent/Ascent (GDA) and Optimistic Gradient Ascent (OGDA). Expand
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A note on approximate Nash equilibria
TLDR
We give a simple, linear-time algorithm examining just two strategies per player and resulting in a 12-approximate Nash equilibrium in any 2-player game. Expand
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The Robust Manifold Defense: Adversarial Training using Generative Models
TLDR
We propose a new type of attack for finding adversarial examples for image classifiers. Expand
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An algorithmic characterization of multi-dimensional mechanisms
TLDR
We show that every feasible, Bayesian, multi-item multi-bidder mechanism for independent, additive bidders can be implemented as a mechanism that: (a) allocates every item independently of the other items; (b) for the allocation of each item it uses a strict ordering of all bbiders' types; and allocates the item using a distribution over hierarchical mechanisms that iron this ordering into a non-strict ordering. Expand
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Strong Duality for a Multiple-Good Monopolist
TLDR
We provide a duality-based framework for revenue maximization in a multiple-good monopoly and prove that the optimal values of these problems are always equal. Expand
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Progress in approximate nash equilibria
TLDR
We give a polynomial algorithm for computing an ε-approximate Nash equilibrium in 2-player games with ε ≈ .38; our algorithm computes equilibria with arbitrarily large supports. Expand
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