Related papers: Two-Timescale Q-Learning with Function Approximati…

This paper resolves the open question of designing near-optimal algorithms for learning imperfect-information extensive-form games from bandit feedback. We present the first line of algorithms that require only…

Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…

This paper investigates the convergence time of log-linear learning to an $\epsilon$-efficient Nash equilibrium in potential games, where an efficient Nash equilibrium is defined as the maximizer of the potential function. Previous…

We study the problem of learning in zero-sum matrix games with repeated play and bandit feedback. Specifically, we focus on developing uncoupled algorithms that guarantee, without communication between players, the convergence of the…

Motivated by their broad applications in reinforcement learning, we study the linear two-time-scale stochastic approximation, an iterative method using two different step sizes for finding the solutions of a system of two equations. Our…

Two player zero sum simultaneous action games are common in video games, financial markets, war, business competition, and many other settings. We first introduce the fundamental concepts of reinforcement learning in two player zero sum…

We propose a framework to compute approximate Nash equilibria in integer programming games with nonlinear payoffs, i.e., simultaneous and non-cooperative games where each player solves a parametrized mixed-integer nonlinear program. We…

We consider the cyber-physical security of parallel server systems, which is relevant for a variety of engineering applications such as networking, manufacturing, and transportation. These systems rely on feedback control and may thus be…

We study a setting in which two players play a (possibly approximate) Nash equilibrium of a bimatrix game, while a learner observes only their actions and has no knowledge of the equilibrium or the underlying game. A natural question is…

In this paper, we apply the idea of fictitious play to design deep neural networks (DNNs), and develop deep learning theory and algorithms for computing the Nash equilibrium of asymmetric $N$-player non-zero-sum stochastic differential…

This paper investigates closed-loop Nash equilibria for discrete-time linear-quadratic (LQ) stochastic nonzero-sum difference games with random coefficients. Unlike existing works, we consider randomness in both state dynamics and cost…

The behaviour of multi-agent learning in competitive settings is often considered under the restrictive assumption of a zero-sum game. Only under this strict requirement is the behaviour of learning well understood; beyond this, learning…

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…

Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite -- is far more…

Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…

One key in real-life Nash equilibrium applications is to calibrate players' cost functions. To leverage the approximation ability of neural networks, we proposed a general framework for optimizing and learning Nash equilibrium using neural…

We study the deterministic and randomized query complexity of finding approximate equilibria in bimatrix games. We show that the deterministic query complexity of finding an $\epsilon$-Nash equilibrium when $\epsilon < \frac{1}{2}$ is…

We propose a two-phase systematical framework for approximation algorithm design and analysis via Lyapunov function. The first phase consists of using Lyapunov function as an input and outputs a continuous-time approximation algorithm with…

There are only a few learning algorithms applicable to stochastic dynamic teams and games which generalize Markov decision processes to decentralized stochastic control problems involving possibly self-interested decision makers. Learning…

We give a quantum algorithm for computing an $\epsilon$-approximate Nash equilibrium of a zero-sum game in a $m \times n$ payoff matrix with bounded entries. Given a standard quantum oracle for accessing the payoff matrix our algorithm runs…