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Related papers: Convex-Concave Min-Max Stackelberg Games

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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…

Optimization and Control · Mathematics 2019-11-01 Maher Nouiehed , Maziar Sanjabi , Tianjian Huang , Jason D. Lee , Meisam Razaviyayn

We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…

Optimization and Control · Mathematics 2020-11-20 Kimon Antonakopoulos , E. Veronica Belmega , Panayotis Mertikopoulos

Min-max optimization problems involving nonconvex-nonconcave objectives have found important applications in adversarial training and other multi-agent learning settings. Yet, no known gradient descent-based method is guaranteed to converge…

Machine Learning · Computer Science 2022-10-19 Constantinos Daskalakis , Noah Golowich , Stratis Skoulakis , Manolis Zampetakis

We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…

Optimization and Control · Mathematics 2009-12-16 Rida Laraki , Jean B. Lasserre

We study Stackelberg equilibria in finitely repeated games, where the leader commits to a strategy that picks actions in each round and can be adaptive to the history of play (i.e. they commit to an algorithm). In particular, we study…

Computer Science and Game Theory · Computer Science 2024-03-08 Natalie Collina , Eshwar Ram Arunachaleswaran , Michael Kearns

We study the problem of finding Stackelberg equilibria in games with a massive number of players. So far, the only known game instances in which the problem is solved in polynomial time are some particular congestion games. However, a…

Computer Science and Game Theory · Computer Science 2019-05-31 Alberto Marchesi , Matteo Castiglioni , Nicola Gatti

The behavior of no-regret learning algorithms is well understood in two-player min-max (i.e, zero-sum) games. In this paper, we investigate the behavior of no-regret learning in min-max games with dependent strategy sets, where the strategy…

Computer Science and Game Theory · Computer Science 2022-04-15 Denizalp Goktas , Jiayi Zhao , Amy Greenwald

Convergence to a saddle point for convex-concave functions has been studied for decades, while recent years has seen a surge of interest in non-convex (zero-sum) smooth games, motivated by their recent wide applications. It remains an…

Machine Learning · Computer Science 2022-02-04 Guojun Zhang , Pascal Poupart , Yaoliang Yu

We study the problem of learning a Nash equilibrium (NE) in Markov games which is a cornerstone in multi-agent reinforcement learning (MARL). In particular, we focus on infinite-horizon adversarial team Markov games (ATMGs) in which agents…

Computer Science and Game Theory · Computer Science 2024-10-10 Fivos Kalogiannis , Jingming Yan , Ioannis Panageas

We study the problem of characterizing the set of games that are consistent with observed equilibrium play. Our contribution is to develop and analyze a new methodology based on convex optimization to address this problem for many classes…

Computer Science and Game Theory · Computer Science 2017-03-23 Juba Ziani , Venkat Chandrasekaran , Katrina Ligett

We study the computational complexity of the problem of computing local min-max equilibria of games with a nonconvex-nonconcave utility function $f$. From the work of Daskalakis, Skoulakis, and Zampetakis [DSZ21], this problem was known to…

Computational Complexity · Computer Science 2026-02-05 Martino Bernasconi , Matteo Castiglioni

Computational advertising has been studied to design efficient marketing strategies that maximize the number of acquired customers. In an increased competitive market, however, a market leader (a leader) requires the acquisition of new…

Computer Science and Game Theory · Computer Science 2019-06-18 Daisuke Hatano , Yuko Kuroki , Yasushi Kawase , Hanna Sumita , Naonori Kakimura , Ken-ichi Kawarabayashi

Designing socially optimal policies in multi-agent environments is a fundamental challenge in both economics and artificial intelligence. This paper studies a general framework for learning Stackelberg equilibria in dynamic and uncertain…

Systems and Control · Electrical Eng. & Systems 2025-09-23 Jun He , Andrew L. Liu , Yihsu Chen

In this paper, we address the problem of interpolation of smooth convex-concave functions. Interpolation is a key step for computer-assisted estimation of worst-case performance via PEP-like techniques, and smooth convex-concave functions…

Optimization and Control · Mathematics 2026-05-26 Valery Krivchenko , Alexander Gasnikov , Dmitry Kovalev

This paper proposes and studies a class of discrete-time finite-time-horizon Stackelberg mean-field games, with one leader and an infinite number of identical and indistinguishable followers. In this game, the objective of the leader is to…

Optimization and Control · Mathematics 2022-10-11 Xin Guo , Anran Hu , Jiacheng Zhang

Recent applications in machine learning have renewed the interest of the community in min-max optimization problems. While gradient-based optimization methods are widely used to solve such problems, there are however many scenarios where…

Optimization and Control · Mathematics 2021-04-15 Sotiris Anagnostidis , Aurelien Lucchi , Youssef Diouane

Stackelberg equilibria have become increasingly important as a solution concept in computational game theory, largely inspired by practical problems such as security settings. In practice, however, there is typically uncertainty regarding…

Computer Science and Game Theory · Computer Science 2017-11-23 Christian Kroer , Gabriele Farina , Tuomas Sandholm

We investigate the computational complexity of min-max optimization under coupled constraints. The work of Daskalakis, Skoulakis, and Zampetakis [DSZ21] was the first to study min-max optimization through the lens of computational…

Computer Science and Game Theory · Computer Science 2026-05-28 Martino Bernasconi , Matteo Castiglioni , Andrea Celli , Gabriele Farina

The Stackelberg equilibrium solution concept describes optimal strategies to commit to: Player 1 (termed the leader) publicly commits to a strategy and Player 2 (termed the follower) plays a best response to this strategy (ties are broken…

Computer Science and Game Theory · Computer Science 2016-08-24 Branislav Bosansky , Simina Branzei , Kristoffer Arnsfelt Hansen , Peter Bro Miltersen , Troels Bjerre Sorensen

Min-max optimization is emerging as a key framework for analyzing problems of robustness to strategically and adversarially generated data. We propose a random reshuffling-based gradient free Optimistic Gradient Descent-Ascent algorithm for…

Optimization and Control · Mathematics 2022-02-22 Chinmay Maheshwari , Chih-Yuan Chiu , Eric Mazumdar , S. Shankar Sastry , Lillian J. Ratliff