Related papers: A policy iteration method for Mean Field Games
In a discrete space and time framework, we study the mean field game limit for a class of symmetric $N$-player games based on the notion of correlated equilibrium. We give a definition of correlated solution that allows to construct…
Most algorithms for solving POMDPs iteratively improve a value function that implicitly represents a policy and are said to search in value function space. This paper presents an approach to solving POMDPs that represents a policy…
The goal of this paper is to show existence of short-time classical solutions to the so called Master Equation of \emph{first order} Mean Field Games, which can be thought of as the limit of the corresponding master equation of a stochastic…
In stochastic dynamic games, when the number of players is sufficiently large and the interactions between agents depend on empirical state distribution, one way to approximate the original game is to introduce infinite-population limit of…
In this article, we study a simplified version of a density-dependent first-order mean field game, in which the players face a penalization equal to the population density at their final position. We consider the problem of finding an…
We study the uniqueness of solutions to systems of PDEs arising in Mean Field Games with several populations of agents and Neumann boundary conditions. The main assumption requires the smallness of some data, e.g., the length of the time…
This thesis investigates the design of algorithms for solving min-max optimization problems, which form the mathematical foundation of many modern applications in machine learning, game theory, and optimization. This work offers new…
The optimization of mixed-variable problems remains a significant challenge. We propose an extension of the policy-based optimization method that handles mixed-variables problems in a natural way, through a simple policy combination. This…
In this paper, we study the portfolio optimization problem formulated by Lacker and Soret. They formulate a finite time horizon model that allows agents to be competitive, measuring their utility not only by their absolute wealth but also…
In this work, we consider policy-based methods for solving the reinforcement learning problem, and establish the sample complexity guarantees. A policy-based algorithm typically consists of an actor and a critic. We consider using various…
We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of…
This note proposes a data-driven output-feedback stabilizing policy iteration for unknown linear discrete-time systems with unmeasurable states. Existing policy iteration methods for optimal control must start from a stabilizing control…
Computing optimal control policies for complex dynamical systems requires approximation methods to remain computationally tractable. Several approximation methods have been developed to tackle this problem. However, these methods do not…
For a general entropy-regularized stochastic control problem on an infinite horizon, we prove that a policy iteration algorithm (PIA) converges to an optimal relaxed control. Contrary to the standard stochastic control literature, classical…
We study stochastic static teams with countably infinite number of decision makers, with the goal of obtaining (globally) optimal policies under a decentralized information structure. We present sufficient conditions to connect the concepts…
We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to…
This letter studies multi-agent reinforcement learning in partially observable Markov potential games. Solving this problem is challenging due to partial observability, decentralized information, and the curse of dimensionality. First, to…
We present examples of equations arising in the theory of mean field games that can be reduced to a system in smaller dimensions. Such examples come up in certain applications, and they can be used as modeling tools to numerically…
A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…
Semi-infinite programming can be used to model a large variety of complex optimization problems. The simple description of such problems comes at a price: semi-infinite problems are often harder to solve than finite nonlinear problems. In…