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Related papers: Non-Monotone Variational Inequalities

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Policy gradient methods enjoy strong practical performance in numerous tasks in reinforcement learning. Their theoretical understanding in multiagent settings, however, remains limited, especially beyond two-player competitive and potential…

Computer Science and Game Theory · Computer Science 2023-12-22 Ioannis Anagnostides , Ioannis Panageas , Gabriele Farina , Tuomas Sandholm

Here, we establish the existence of weak solutions to a wide class of time-dependent monotone mean-field games (MFGs). These MFGs are given as a system of degenerate parabolic equations with initial and terminal conditions. To construct…

Analysis of PDEs · Mathematics 2020-01-14 Rita Ferreira , Diogo Gomes , Teruo Tada

In this paper we consider strong Nash equilibria, in mixed strategies, for finite games. Any strong Nash equilibrium outcome is Pareto efficient for each coalition. First, we analyze the two--player setting. Our main result, in its simplest…

Optimization and Control · Mathematics 2015-03-02 Eleonora Braggion , Nicola Gatti , Roberto Lucchetti , Tuomas Sandholm

We consider parity games on infinite graphs where configurations are represented by control-states and integer vectors. This framework subsumes two classic game problems: parity games on vector addition systems with states (vass) and…

Logic in Computer Science · Computer Science 2013-06-13 Parosh Aziz Abdulla , Richard Mayr , Arnaud Sangnier , Jeremy Sproston

In this paper, we present a novel stochastic method for solving variational inequalities (VI) in the context of Markovian noise. By leveraging Extragradient technique, we can productively solve VI optimization problems characterized by…

Optimization and Control · Mathematics 2026-05-18 Vladimir Solodkin , Michael Ermoshin , Roman Gavrilenko , Aleksandr Beznosikov

In this article we consider a special class of Nash equilibrium problems that cannot be reduced to a single player control problem. Problems of this type can be solved by a semi-smooth Newton method. Applying results from the established…

Optimization and Control · Mathematics 2018-11-09 Veronika Karl , Frank Pörner

Games with incomplete preferences are an important model for studying rational decision-making in scenarios where players face incomplete information about their preferences and must contend with incomparable outcomes. We study the problem…

Computer Science and Game Theory · Computer Science 2024-08-13 Abhishek N. Kulkarni , Jie Fu , Ufuk Topcu

We study nested variational inequalities, which are variational inequalities whose feasible set is the solution set of another variational inequality. We present a projected averaging Tikhonov algorithm requiring the weakest conditions in…

Optimization and Control · Mathematics 2021-12-20 Lorenzo Lampariello , Gianluca Priori , Simone Sagratella

We address the numerical approximation of Mean Field Games with local couplings. For power-like Hamiltonians, we consider both unconstrained and constrained stationary systems with density constraints in order to model hard congestion…

Optimization and Control · Mathematics 2019-02-08 L. M. Briceño-Arias , D. Kalise , F. J. Silva

In a normed space setting, this paper studies the conditions under which the projected solutions to a quasi equilibrium problem with non-self constraint map exist. Our approach is based on an iterative algorithm which gives rise to a…

Optimization and Control · Mathematics 2023-09-06 Monica Bianchi , Enrico Miglierina , Maede Ramazannejad

The standard risk minimization paradigm of machine learning is brittle when operating in environments whose test distributions are different from the training distribution due to spurious correlations. Training on data from many…

Machine Learning · Computer Science 2020-03-20 Kartik Ahuja , Karthikeyan Shanmugam , Kush R. Varshney , Amit Dhurandhar

The optimization problems associated with training generative adversarial neural networks can be largely reduced to certain {\em non-monotone} variational inequality problems (VIPs), whereas existing convergence results are mostly based on…

Optimization and Control · Mathematics 2021-03-09 Chaobing Song , Zhengyuan Zhou , Yichao Zhou , Yong Jiang , Yi Ma

Nash equilibrium} (NE) can be stated as a formal theorem on a multilinear form, free of game theory terminology. On the other hand, inspired by this formalism, we state and prove a {\it multilinear minimax theorem}, a generalization of von…

Computer Science and Game Theory · Computer Science 2024-01-01 Bahman Kalantari

This paper introduces the concept of perfect monotone equilibrium in Bayesian games, which refines the standard monotone equilibrium by accounting for the possibility of unintended moves (trembling hand) and thereby enhancing robustness to…

Theoretical Economics · Economics 2025-10-16 Wei He , Yeneng Sun , Hanping Xu

We study episodic two-player zero-sum Markov games (MGs) in the offline setting, where the goal is to find an approximate Nash equilibrium (NE) policy pair based on a dataset collected a priori. When the dataset does not have uniform…

Machine Learning · Computer Science 2023-01-02 Han Zhong , Wei Xiong , Jiyuan Tan , Liwei Wang , Tong Zhang , Zhaoran Wang , Zhuoran Yang

We study generalized games defined over Banach spaces using variational analysis. To reformulate generalized games as quasi-variational inequality problems, we will first form a suitable principal operator and study some significant…

Optimization and Control · Mathematics 2024-07-29 Asrifa Sultana , Shivani Valecha

Algorithms that solve zero-sum games, multi-objective agent objectives, or, more generally, variational inequality (VI) problems are notoriously unstable on general problems. Owing to the increasing need for solving such problems in machine…

Machine Learning · Statistics 2022-07-15 Tatjana Chavdarova , Ya-Ping Hsieh , Michael I. Jordan

Using the KKM technique, we establish some existence results for variational-hemivariational inequalities involving monotone set valued mappings on bounded, closed and convex subsets in reflexive Banach spaces. We also derive several…

Classical Analysis and ODEs · Mathematics 2009-09-09 Nicusor Costea , Cezar Lupu

We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and…

Probability · Mathematics 2018-12-04 Enzo Miller , Huyen Pham

This paper makes progress towards learning Nash equilibria in two-player zero-sum Markov games from offline data. Specifically, consider a $\gamma$-discounted infinite-horizon Markov game with $S$ states, where the max-player has $A$…

Machine Learning · Computer Science 2025-03-18 Yuling Yan , Gen Li , Yuxin Chen , Jianqing Fan