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Motivated by the omnipresence of hierarchical structures in many real-world applications, this study delves into the intricate realm of bi-level games, with a specific focus on exploring local Stackelberg equilibria as a solution concept.…

In a Stackelberg congestion game (SCG), a leader aims to maximize their own gain by anticipating and manipulating the equilibrium state at which the followers settle by playing a congestion game. Often formulated as bilevel programs,…

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…

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…

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…

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…

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…

The Stackelberg game depicts a leader-follower relationship wherein decisions are made sequentially, and the Stackelberg equilibrium represents an expected optimal solution when the leader can anticipate the rational response of the…

Stackelberg Games are gaining importance in the last years due to the raise of Adversarial Machine Learning (AML). Within this context, a new paradigm must be faced: in classical game theory, intervening agents were humans whose decisions…

In this paper, we develop an approximation scheme for solving bilevel programs with equilibrium constraints, which are generally difficult to solve. Among other things, calculating the first-order derivative in such a problem requires…

Understanding and analyzing markets is crucial, yet analytical equilibrium solutions remain largely infeasible. Recent breakthroughs in equilibrium computation rely on zeroth-order policy gradient estimation. These approaches commonly…

Bilevel optimization has arisen as a powerful tool in modern machine learning. However, due to the nested structure of bilevel optimization, even gradient-based methods require second-order derivative approximations via Jacobian- or/and…

Bilevel optimization has been applied to a wide variety of machine learning models, and numerous stochastic bilevel optimization algorithms have been developed in recent years. However, most existing algorithms restrict their focus on the…

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

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.…

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…

We investigate a co-design problem, encompassing simultaneous design of system infrastructure and control, through a game-theoretical framework. To this end, we propose the co-design problem as a two-layer hierarchical strategic…

Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…

Motivated by the increasing attention to overall social benefits in networked multi-agent systems, this paper investigates an optimization problem building on noncooperative games under high-level regulation, which can be formulated in a…

The success of adversarial formulations in machine learning has brought renewed motivation for smooth games. In this work, we focus on the class of stochastic Hamiltonian methods and provide the first convergence guarantees for certain…