Related papers: First-order (coarse) correlated equilibria in non-…

We consider a class of smooth $N$-player noncooperative games, where player objectives are expectation-valued and potentially nonconvex. In such a setting, we consider the largely open question of efficiently computing a suitably defined…

We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…

The framework of multi-agent learning explores the dynamics of how individual agent strategies evolve in response to the evolving strategies of other agents. Of particular interest is whether or not agent strategies converge to well known…

We develop a unified theory of augmented Lagrangians for nonconvex optimization problems that encompasses both duality theory and convergence analysis of primal-dual augmented Lagrangian methods in the infinite dimensional setting. Our goal…

In many multiagent settings, such as electric vehicle charging and traffic routing, agents must make decisions in the face of uncertain behavior exhibited by others. Often, this uncertainty arises from multiple sources, such as incomplete…

We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in…

In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…

Nash equilibrium is a central concept in game theory. Several Nash solvers exist, yet none scale to normal-form games with many actions and many players, especially those with payoff tensors too big to be stored in memory. In this work, we…

We introduce the application of online learning in a Stackelberg game pertaining to a system with two learning agents in a dyadic exchange network, consisting of a supplier and retailer, specifically where the parameters of the demand…

Sharpness is an almost generic assumption in continuous optimization that bounds the distance from minima by objective function suboptimality. It facilitates the acceleration of first-order methods through restarts. However, sharpness…

In decision-dependent games, multiple players optimize their decisions under a data distribution that shifts with their joint actions, creating complex dynamics in applications like market pricing. A practical consequence of these dynamics…

Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…

We study coordination mechanisms for Scheduling Games (with unrelated machines). In these games, each job represents a player, who needs to choose a machine for its execution, and intends to complete earliest possible. Our goal is to design…

In this paper we focus on the problem of Online Principal Component Analysis in the regret minimization framework. For this problem, all existing regret minimization algorithms for the fully-adversarial setting are based on a positive…

An active line of research has considered games played on networks in which payoffs depend on both a player's individual decision and also the decisions of her neighbors. Such games have been used to model issues including the formation of…

We introduce a new form of Lagrangian and propose a simple first-order algorithm for nonconvex optimization with nonlinear equality constraints. We show the algorithm generates bounded dual iterates, and establish the convergence to KKT…

The study of first-order optimization is sensitive to the assumptions made on the objective functions. These assumptions induce complexity classes which play a key role in worst-case analysis, including the fundamental concept of algorithm…

Sparse iterative methods, in particular first-order methods, are known to be among the most effective in solving large-scale two-player zero-sum extensive-form games. The convergence rates of these methods depend heavily on the properties…

We study assignment games in which jobs select machines, and in which certain pairs of jobs may conflict, which is to say they may incur an additional cost when they are both assigned to the same machine, beyond that associated with the…

Classical global convergence results for first-order methods rely on uniform smoothness and the \L{}ojasiewicz inequality. Motivated by properties of objective functions that arise in machine learning, we propose a non-uniform refinement of…