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We propose the first loss function for approximate Nash equilibria of normal-form games that is amenable to unbiased Monte Carlo estimation. This construction allows us to deploy standard non-convex stochastic optimization techniques for…
We consider generalized Nash equilibrium (GNE) problems in games with strongly monotone pseudo-gradients and jointly linear coupling constraints. We establish the convergence rate of a payoff-based approach intended to learn a variational…
Pseudo-games are a natural and well-known generalization of normal-form games, in which the actions taken by each player affect not only the other players' payoffs, as in games, but also the other players' strategy sets. The solution…
This paper considers convex games involving multiple agents that aim to minimize their own cost functions using locally available information. A common assumption in the study of such games is that the agents are symmetric, meaning that…
In this paper, we consider a distributed learning problem in a subnetwork zero-sum game, where agents are competing in different subnetworks. These agents are connected through time-varying graphs where each agent has its own cost function…
This paper investigates stochastic generalized dynamic games with coupling chance constraints, where agents have incomplete information about uncertainties satisfying a concentration of measure property. This problem, in general, is…
Understanding the convergence landscape of multi-agent learning is a fundamental problem of great practical relevance in many applications of artificial intelligence and machine learning. While it is known that learning dynamics converge to…
Many supervised machine learning methods are naturally cast as optimization problems. For prediction models which are linear in their parameters, this often leads to convex problems for which many mathematical guarantees exist. Models which…
We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially…
Network games provide a powerful framework for modeling agent interactions in networked systems, where players are represented by nodes in a graph and their payoffs depend on the actions taken by their neighbors. Extending the framework of…
Smooth game optimization has recently attracted great interest in machine learning as it generalizes the single-objective optimization paradigm. However, game dynamics is more complex due to the interaction between different players and is…
The Nash equilibrium is an important benchmark for behaviour in systems of strategic autonomous agents. Polymatrix games are a succinct and expressive representation of multiplayer games that model pairwise interactions between players. The…
Fitting a function by using linear combinations of a large number $N$ of `simple' components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to…
Systems of competing agents can often be modeled as games. Assuming rationality, the most likely outcomes are given by an equilibrium (e.g. a Nash equilibrium). In many practical settings, games are influenced by context, i.e. additional…
In the first part of this dissertation research, we develop a modular framework that can serve as a recipe for constructing and analyzing iterative algorithms for convex optimization. Specifically, our work casts optimization as iteratively…
We present a general framework for solving a large class of learning problems with non-linear functions of classification rates. This includes problems where one wishes to optimize a non-decomposable performance metric such as the F-measure…
One of the mysteries in the success of neural networks is randomly initialized first order methods like gradient descent can achieve zero training loss even though the objective function is non-convex and non-smooth. This paper demystifies…
In this paper, a gentle introduction to Game Theory is presented in the form of basic concepts and examples. Minimax and Nash's theorem are introduced as the formal definitions for optimal strategies and equilibria in zero-sum and…
The two-timescale gradient descent-ascent (GDA) is a canonical gradient algorithm designed to find Nash equilibria in min-max games. We analyze the two-timescale GDA by investigating the effects of learning rate ratios on convergence…
Several works have shown unconditional hardness (via integrality gaps) of computing equilibria using strong hierarchies of convex relaxations. Such results however only apply to the problem of computing equilibria that optimize a certain…