We study a heterogeneous agent macroeconomic model with an infinite number of households and firms competing in a labor market. Each household earns income and engages in consumption at each time step while aiming to maximize a concave utility subject to the underlying market conditions. The households aim to find the optimal saving strategy that maximizes their discounted cumulative utility given the market condition, while the firms determine the market conditions through maximizing corporate profit based on the household population behavior. The model captures a wide range of applications in macroeconomic studies, and we propose a data-driven reinforcement learning framework that finds the regularized competitive equilibrium of the model. The proposed algorithm enjoys theoretical guarantees in converging to the equilibrium of the market at a sub-linear rate.
Mastercard Corporation（万事达卡公司）；Georgia Institute of Technology（佐治亚理工学院）
We explore the use of policy approximations to reduce the computational cost of learning Nash equilibria in zero-sum stochastic games. We propose a new Q-learning type algorithm that uses a sequence of entropy-regularized soft policies to approximate the Nash policy during the Q-function updates. We prove that under certain conditions, by updating the regularized Q-function, the algorithm converges to a Nash equilibrium. We also demonstrate the proposed algorithm's ability to transfer previous training experiences, enabling the agents to adapt quickly to new environments. We provide a dynamic …
National Technical University of Athens（雅典国立技术大学）；Columbia University（哥伦比亚大学）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；Criteo AI Lab（Criteo人工智能实验室）
In this paper, we examine the Nash equilibrium convergence properties of no-regret learning in general N-player games. For concreteness, we focus on the archetypal follow the regularized leader (FTRL) family of algorithms, and we consider the full spectrum of uncertainty that the players may encounter - from noisy, oracle-based feedback, to bandit, payoff-based information. In this general context, we establish a comprehensive equivalence between the stability of a Nash equilibrium and its support: a Nash equilibrium is stable and attracting with arbitrarily high probability if and only if it …
Real economies can be modeled as a sequential imperfect-information game with many heterogeneous agents, such as consumers, firms, and governments. Dynamic general equilibrium (DGE) models are often used for macroeconomic analysis in this setting. However, finding general equilibria is challenging using existing theoretical or computational methods, especially when using microfoundations to model individual agents. Here, we show how to use deep multi-agent reinforcement learning (MARL) to find $ε$-meta-equilibria over agent types in microfounded DGE models. Whereas standard MARL fails to learn…
The recent mean field game (MFG) formalism facilitates otherwise intractable computation of approximate Nash equilibria in many-agent settings. In this paper, we consider discrete-time finite MFGs subject to finite-horizon objectives. We show that all discrete-time finite MFGs with non-constant fixed point operators fail to be contractive as typically assumed in existing MFG literature, barring convergence via fixed point iteration. Instead, we incorporate entropy-regularization and Boltzmann policies into the fixed point iteration. As a result, we obtain provable convergence to approximate fi…
Recent advances at the intersection of dense large graph limits and mean field games have begun to enable the scalable analysis of a broad class of dynamical sequential games with large numbers of agents. So far, results have been largely limited to graphon mean field systems with continuous-time diffusive or jump dynamics, typically without control and with little focus on computational methods. We propose a novel discrete-time formulation for graphon mean field games as the limit of non-linear dense graph Markov games with weak interaction. On the theoretical side, we give extensive and rigo…
Entropy-Regularized Reinforcement Learning for Linear-Quadratic Stackelberg Differential Games in Regime-Switching Diffusion Models
School of Mathematics and Statistics, Anhui Normal University（安徽师范大学数学与统计学学院）；School of Statistics, Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, Faculty of Economics and Management, East China Normal University（东华大学统计学院）；School of Mathematics, Southeast University（东南大学数学学院）
Robust Adversarial Reinforcement Learning via Bounded Rationality Curricula
TU Darmstadt（达姆施塔特工业大学）；Hessian Center for Artificial Intelligence (Hessian.ai)（黑森人工智能中心）；German Research Center for AI (DFKI)（德国人工智能研究中心）；University of Magdeburg（马格德堡大学）；JLU Gießen（吉森大学）；University of Würzburg（维尔茨堡大学）
University of Pennsylvania（宾夕法尼亚大学）；Carnegie Mellon University（卡内基梅隆大学）
This paper studies multi-agent reinforcement learning in Markov games, with the goal of learning Nash equilibria or coarse correlated equilibria (CCE) sample-optimally. All prior results suffer from at least one of the two obstacles: the curse of multiple agents and the barrier of long horizon, regardless of the sampling protocol in use. We take a step towards settling this problem, assuming access to a flexible sampling mechanism: the generative model. Focusing on non-stationary finite-horizon Markov games, we develop a fast learning algorithm called \myalg~and an adaptive sampling scheme tha…
The Power of Regularization in Solving Extensive-Form Games
Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；LIDS, EECS, Massachusetts Institute of Technology（麻省理工学院信息学院）；University of Maryland, College Park（马里兰大学帕克分校）
