相关论文: Discretization Drift in Two-Player Games

We study convergence rates of the generalized conditional gradient (GCG) method applied to fully discretized Mean Field Games (MFG) systems. While explicit convergence rates of the GCG method have been established at the continuous PDE…

This article focuses two issues related to the first-order discounted mean field games system. The first is the time discretization problem. The time discretization approach enables us to prove the existence of solutions (u,m) of the…

The two-timescale gradient descent-ascent (GDA) is a canonical gradient algorithm designed to find Nash equilibria in min-max games. We analyze the two-timescale GDA by investigating the effects of learning rate ratios on convergence…

Discretization of phase space usually nullifies chaos in dynamical systems. We show that if randomness is associated with discretization dynamical chaos may survive and be indistinguishable from that of the original chaotic system, when an…

We analyze inertial coordination games: dynamic coordination games with an endogenously changing state that depends on (i) a persistent fundamental players privately learn about over time; and (ii) past play. The speed of learning…

The perceived risk and reward for a given situation can vary depending on resource availability, accumulated wealth, and other extrinsic factors such as individual backgrounds. Based on this general aspect of everyday life, here we use…

Generative Adversarial Networks (GANs) have shown remarkable performance in image generation. However, GAN training suffers from the problem of instability. One of the main approaches to address this problem is to modify the loss function,…

Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization --…

We study two-player security games which can be viewed as sequences of nonzero-sum matrix games played by an Attacker and a Defender. The evolution of the game is based on a stochastic fictitious play process. Players do not have access to…

Dual gradient descent combined with early stopping represents an efficient alternative to the Tikhonov variational approach when the regularizer is strongly convex. However, for many relevant applications, it is crucial to deal with…

In this paper we consider the problem of distributed Nash equilibrium (NE) seeking over networks, a setting in which players have limited local information. We start from a continuous-time gradient-play dynamics that converges to an NE…

Consider a two-player game repeated N times. Player 1 can choose between two styles (for interpretability, offensive and defensive), whereas Player 2 uses a single fixed style. Let X N\,:= \#wins -\#losses for Player 1 after N games, and…

The rapid progress in machine learning in recent years has been based on a highly productive connection to gradient-based optimization. Further progress hinges in part on a shift in focus from pattern recognition to decision-making and…

The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…

Generating competitive strategies and performing continuous motion planning simultaneously in an adversarial setting is a challenging problem. In addition, understanding the intent of other agents is crucial to deploying autonomous systems…

This work explores three-player game training dynamics, under what conditions three-player games converge and the equilibria the converge on. In contrast to prior work, we examine a three-player game architecture in which all players…

Adversarial training often suffers from a robustness-accuracy trade-off, where achieving high robustness comes at the cost of accuracy. One approach to mitigate this trade-off is leveraging invariance regularization, which encourages model…

We present a fast numerical algorithm for large scale zero-sum stochastic games with perfect information, which combines policy iteration and algebraic multigrid methods. This algorithm can be applied either to a true finite state space…

We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…

The dominant line of work in domain adaptation has focused on learning invariant representations using domain-adversarial training. In this paper, we interpret this approach from a game theoretical perspective. Defining optimal solutions in…