Related papers: Convex-Concave Min-Max Stackelberg Games
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…
Zero-sum Markov Stackelberg games can be used to model myriad problems, in domains ranging from economics to human robot interaction. In this paper, we develop policy gradient methods that solve these games in continuous state and action…
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…
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…
Stackelberg games originate where there are market leaders and followers, and the actions of leaders influence the behavior of the followers. Mathematical modelling of such games results in what's called a Bilevel Optimization problem.…
Solving feedback Stackelberg games with nonlinear dynamics and coupled constraints, a common scenario in practice, presents significant challenges. This work introduces an efficient method for computing approximate local feedback…
Stackelberg games have been widely used to model interactive decision-making problems in a variety of domains such as energy systems, transportation, cybersecurity, and human-robot interaction. However, existing algorithms for solving…
We contribute the first provable guarantees of global convergence to Nash equilibria (NE) in two-player zero-sum convex Markov games (cMGs) by using independent policy gradient methods. Convex Markov games, recently defined by Gemp et al.…
The min-max optimization problem, also known as the saddle point problem, is a classical optimization problem which is also studied in the context of zero-sum games. Given a class of objective functions, the goal is to find a value for the…
Differential games, in particular two-player sequential zero-sum games (a.k.a. minimax optimization), have been an important modeling tool in applied science and received renewed interest in machine learning due to many recent applications,…
Minimax optimization has been central in addressing various applications in machine learning, game theory, and control theory. Prior literature has thus far mainly focused on studying such problems in the continuous domain, e.g.,…
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…
Min-max optimization problems arise in several key machine learning setups, including adversarial learning and generative modeling. In their general form, in absence of convexity/concavity assumptions, finding pure equilibria of the…
Hierarchical decision making problems, such as bilevel programs and Stackelberg games, are attracting increasing interest in both the engineering and machine learning communities. Yet, existing solution methods lack either convergence…
Stackelberg games are a classic example of bilevel optimization problems, which are often encountered in game theory and economics. These are complex problems with a hierarchical structure, where one optimization task is nested within the…
Min-max problems have broad applications in machine learning, including learning with non-decomposable loss and learning with robustness to data distribution. Convex-concave min-max problem is an active topic of research with efficient…
Min-max optimization problems, also known as saddle point problems, have attracted significant attention due to their applications in various fields, such as fair beamforming, generative adversarial networks (GANs), and adversarial…
Stackelberg equilibrium is a solution concept that describes optimal strategies to commit: Player 1 (the leader) first commits to a strategy that is publicly announced, then Player 2 (the follower) plays a best response to the leader's…
This paper considers minimax optimization $\min_x \max_y f(x, y)$ in the challenging setting where $f$ can be both nonconvex in $x$ and nonconcave in $y$. Though such optimization problems arise in many machine learning paradigms including…
In the literature on game-theoretic equilibrium finding, focus has mainly been on solving a single game in isolation. In practice, however, strategic interactions -- ranging from routing problems to online advertising auctions -- evolve…