arXiv research

Gradient methods converge exponentially in concave network games.

Study Nash equilibrium in non-zero-sum game with Bermudan strategies.

Just as war is sometimes fallaciously represented as a zero sum game -- when in fact war is a negative sum game - stock market trading, a positive sum game over time, is often erroneously represented as a zero sum game. This is called the "zero sum fallacy" -- the erroneous belief that one trader in a stock market exch…

New algorithm finds near-optimal policies efficiently in zero-sum games.

Gradient Descent Ascent converges to von-Neumann solution in hidden zero-sum games.

Paper studies competitive networks where teams aim to minimize their own objectives, adapting to each other's strategies.

Study proposes new OPE estimators for two-player zero-sum games.

ZeroS improves Transformers by adding negative weights, matching or beating softmax attention.

Paper proposes a mean-field gradient descent for zero-sum games, proving convergence to Nash equilibrium.

Study on convergence of Langevin dynamics for zero-sum games in probability distributions.

New assumptions and algorithm solve offline two-player zero-sum Markov games.

Mutation improves FTRL convergence in zero-sum games.

This work finds mixed equilibria in zero-sum games using interacting particle dynamics.

New approach improves robustness of deep neural networks without overfitting.

We consider the problem of two-player zero-sum games. This problem is formulated as a min-max Markov game in the literature. The solution of this game, which is the min-max payoff, starting from a given state is called the min-max value of the state. In this work, we compute the solution of the two-player zero-sum game…

Zero-sum games have long guided artificial intelligence research, since they possess both a rich strategy space of best-responses and a clear evaluation metric. What's more, competition is a vital mechanism in many real-world multi-agent systems capable of generating intelligent innovations: Darwinian evolution, the ma…

Study best-response learning dynamics in zero-sum polymatrix games under full and minimal information settings.

New algorithms converge faster to Nash equilibrium in zero-sum games with bandit feedback.

Paper studies zero-sum games with noisy observations and identifies equilibrium conditions.

We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave saddle-point problem in the policy space. Specifically, we show that despite its nonconve…

New game approximates mean curvature flow evolution.

Algorithm learns from changing zero-sum games with no regret.

Paper develops efficient algorithms for zero-sum Markov games with general function classes.

Study of $2 imes 2$ zero-sum games with noisy observations and commitments.

Algorithm learns Nash equilibria in stochastic games using entropy-regularized policies.

Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several benchmark learning tasks, GAN minimax optimization still poses great theoretical and…

Paper studies constrained control games with a novel approximation method.

The paper solves investment problems with uncertain factors using game theory.

Zero-sum games such as chess and poker are, abstractly, functions that evaluate pairs of agents, for example labeling them `winner' and `loser'. If the game is approximately transitive, then self-play generates sequences of agents of increasing strength. However, nontransitive games, such as rock-paper-scissors, can ex…

We study a wide class of non-convex non-concave min-max games that generalizes over standard bilinear zero-sum games. In this class, players control the inputs of a smooth function whose output is being applied to a bilinear zero-sum game. This class of games is motivated by the indirect nature of the competition in Ge…

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 grand challenge. As a first step, we restrict to bilinear zero-sum games and giv…

Study learns optimal strategies in imperfect information games with self-play.

This paper studies a 2-players zero-sum Dynkin game arising from pricing an option on an asset whose rate of return is unknown to both players. Using filtering techniques we first reduce the problem to a zero-sum Dynkin game on a bi-dimensional diffusion $(X,Y)$. Then we characterize the existence of a Nash equilibrium…

Game-theoretic models of learning are a powerful set of models that optimize multi-objective architectures. Among these models are zero-sum architectures that have inspired adversarial learning frameworks. An important shortcoming of these zeros-sum architectures is that gradient-based training leads to weak convergenc…

We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop. Moreover, each player can adjust her own stopping strategy according to the other player's action. In the first part of the paper, we consider the game wh…

In this paper we study Backward Stochastic Differential Equations with two reflecting right continuous with left limits obstacles (or barriers) when the noise is given by Brownian motion and a Poisson random measure mutually independent. The jumps of the obstacle processes could be either predictable or inaccessible. W…

Exchanges acquire excess processing capacity to accommodate trading activity surges associated with zero-sum high-frequency trader (HFT) "duels." The idle capacity's opportunity cost is an externality of low-latency trading. We build a model of decentralized exchanges (DEX) with flexible capacity. On DEX, HFTs acquire …

Optimistic Hedge achieves optimal regret bounds in two-player zero-sum games.

Let $U/K_Θ$ be a generalized flag manifold, where $K_Θ$ is the centralizer of a torus in $U$. We study $U$-invariant almost Hermitian structures on $U/K_Θ$. The classification of these structures are naturally related with the system $R_t$ of t-roots associated to $U/K_Θ$. We introduced the notion of connectedness by t…

We consider a symmetric multi-players zero-sum game with two strategic variables. There are $n$ players, $n\geq 3$. Each player is denoted by $i$. Two strategic variables are $t_i$ and $s_i$, $i\in \{1, \dots, n\}$. They are related by invertible functions. Using the minimax theorem by \cite{sion} we will show that Nas…

Optimal algorithm for two-player zero-sum games with linear parameterization.

Paper solves complex game theory problems with new equations.

New algorithm improves sample efficiency for zero-sum Markov games.

In this paper we investigate the Follow the Regularized Leader dynamics in sequential imperfect information games (IIG). We generalize existing results of Poincaré recurrence from normal-form games to zero-sum two-player imperfect information games and other sequential game settings. We then investigate how adapting th…

Pessimistic model-based algorithm finds Nash equilibria in zero-sum Markov games from offline data.

We address the issue of limit cycling behavior in training Generative Adversarial Networks and propose the use of Optimistic Mirror Decent (OMD) for training Wasserstein GANs. Recent theoretical results have shown that optimistic mirror decent (OMD) can enjoy faster regret rates in the context of zero-sum games. WGANs …

We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum game is core to many problems in statistics, optimization, and economics, and fo…

Paper analyzes robust strategies in a pension plan game with ambiguous financial markets.