Related papers: Gradient Descent Ascent in Min-Max Stackelberg Gam…
A major approach to saddle point optimization $\min_x\max_y f(x, y)$ is a gradient based approach as is popularized by generative adversarial networks (GANs). In contrast, we analyze an alternative approach relying only on an oracle that…
The Stackelberg game model, where a leader commits to a strategy and the follower best responds, has found widespread application, particularly to security problems. In the security setting, the goal is for the leader to compute an optimal…
Finding Nash equilibria in two-player zero-sum continuous games is a central problem in machine learning, e.g. for training both GANs and robust models. The existence of pure Nash equilibria requires strong conditions which are not…
Under mild regularity conditions, gradient-based methods converge globally to a critical point in the single-loss setting. This is known to break down for vanilla gradient descent when moving to multi-loss optimization, but can we hope to…
Multi-robot coordination often exhibits hierarchical structure, with some robots' decisions depending on the planned behaviors of others. While game theory provides a principled framework for such interactions, existing solvers struggle to…
Learning and computation of equilibria are central problems in game theory, theory of computation, and artificial intelligence. In this work, we introduce proximal regret, a new notion of regret based on proximal operators that lies…
Current research applying N-level Stackelberg Game to multi-agent systems often uses the default decision order of agents provided by the environment. However, this raises the question: does the order of agents necessarily affect the final…
In this paper, the problem of distributively seeking the equilibria of aggregative games with bilevel structures is studied. Different from the traditional aggregative games, here the aggregation is determined by the minimizer of a virtual…
In this paper, the problem of seeking optimal distributed resource allocation (DRA) policies on cellular networks in the presence of an unknown malicious adding-edge attacker is investigated. This problem is described as the games of games…
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…
Contemporary applications of machine learning in two-team e-sports and the superior expressivity of multi-agent generative adversarial networks raise important and overlooked theoretical questions regarding optimization in two-team games.…
Many economic games and machine learning approaches can be cast as competitive optimization problems where multiple agents are minimizing their respective objective function, which depends on all agents' actions. While gradient descent is a…
We study the performance of the gradient play algorithm for stochastic games (SGs), where each agent tries to maximize its own total discounted reward by making decisions independently based on current state information which is shared…
In this paper, we study a large-scale multi-agent minimax optimization problem, which models many interesting applications in statistical learning and game theory, including Generative Adversarial Networks (GANs). The overall objective is a…
Last-iterate convergence has received extensive study in two player zero-sum games starting from bilinear, convex-concave up to settings that satisfy the MVI condition. Typical methods that exhibit last-iterate convergence for the…
Distributed optimization and Nash equilibrium (NE) seeking problems have drawn much attention in the control community recently. This paper studies a class of non-cooperative games, known as N-cluster game, which subsumes both cooperative…
In this work, a novel Stackelberg game theoretic framework is proposed for trading energy bidirectionally between the demand-response (DR) aggregator and the prosumers. This formulation allows for flexible energy arbitrage and additional…
We address the generalized Nash equilibrium seeking problem in a partial-decision information scenario, where each agent can only exchange information with some neighbors, although its cost function possibly depends on the strategies of all…
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…
This work studies Nash equilibrium seeking for a class of stochastic aggregative games, where each player has an expectation-valued objective function depending on its local strategy and the aggregate of all players' strategies. We propose…