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Many recent AI architectures are inspired by zero-sum games, however, the behavior of their dynamics is still not well understood. Inspired by this, we study standard gradient descent ascent (GDA) dynamics in a specific class of non-convex…

A seminal result in game theory is von Neumann's minmax theorem, which states that zero-sum games admit an essentially unique equilibrium solution. Classical learning results build on this theorem to show that online no-regret dynamics…

Min-max saddle point games appear in a wide range of applications in machine leaning and signal processing. Despite their wide applicability, theoretical studies are mostly limited to the special convex-concave structure. While some recent…

Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, while understanding the dynamics of gradient algorithms for solving such formulations has remained a…

Many emerging applications - such as adversarial training, AI alignment, and robust optimization - can be framed as zero-sum games between neural nets, with von Neumann-Nash equilibria (NE) capturing the desirable system behavior. While…

We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash…

Zero-sum and non-zero-sum (aka general-sum) games are relevant in a wide range of applications. While general non-zero-sum games are computationally hard, researchers focus on the special class of monotone games for gradient-based…

Adversarial training, a special case of multi-objective optimization, is an increasingly prevalent machine learning technique: some of its most notable applications include GAN-based generative modeling and self-play techniques in…

In this paper we study two-player bilinear zero-sum games with constrained strategy spaces. An instance of natural occurrences of such constraints is when mixed strategies are used, which correspond to a probability simplex constraint. We…

Replicator dynamics, the continuous-time analogue of Multiplicative Weights Updates, is the main dynamic in evolutionary game theory. In simple evolutionary zero-sum games, such as Rock-Paper-Scissors, replicator dynamic is periodic…

Motivated by Generative Adversarial Networks, we study the computation of Nash equilibrium in concave network zero-sum games (NZSGs), a multiplayer generalization of two-player zero-sum games first proposed with linear payoffs. Extending…

Recent applications that arise in machine learning have surged significant interest in solving min-max saddle point games. This problem has been extensively studied in the convex-concave regime for which a global equilibrium solution can be…

Minimax problems of the form $\min_x \max_y \Psi(x,y)$ have attracted increased interest largely due to advances in machine learning, in particular generative adversarial networks. These are typically trained using variants of stochastic…

We study the convergence of Optimistic Gradient Descent Ascent in unconstrained bilinear games. In a first part, we consider the zero-sum case and extend previous results by Daskalakis et al. in 2018, Liang and Stokes in 2019, and others:…

Adaptive momentum methods have recently attracted a lot of attention for training of deep neural networks. They use an exponential moving average of past gradients of the objective function to update both search directions and learning…

In this work, we establish near-linear and strong convergence for a natural first-order iterative algorithm that simulates Von Neumann's Alternating Projections method in zero-sum games. First, we provide a precise analysis of Optimistic…

We focus on the design of algorithms for finding equilibria in 2-player zero-sum games. Although it is well known that such problems can be solved by a single linear program, there has been a surge of interest in recent years for simpler…

In this short note, we consider the problem of solving a min-max zero-sum game. This problem has been extensively studied in the convex-concave regime where the global solution can be computed efficiently. Recently, there have also been…

The predominant paradigm in evolutionary game theory and more generally online learning in games is based on a clear distinction between a population of dynamic agents that interact given a fixed, static game. In this paper, we move away…

Min-max optimization problems (i.e., min-max games) have attracted a great deal of attention recently as their applicability to a wide range of machine learning problems has become evident. In this paper, we study min-max games with…