Related papers: A policy iteration method for Mean Field Games
In the literature, existence of mean-field equilibria has been established for discrete-time mean field games under both the discounted cost and the average cost optimality criteria. In this paper, we provide a value iteration algorithm to…
Optimal policies in standard MDPs can be obtained using either value iteration or policy iteration. However, in the case of zero-sum Markov games, there is no efficient policy iteration algorithm; e.g., it has been shown that one has to…
We consider a deterministic mean field games problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect…
Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has…
In this paper, we propose a new policy iteration algorithm to compute the value function and the optimal controls of continuous time stochastic control problems. The algorithm relies on successive approximations using linear-quadratic…
Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely large populations of agents. Yet, most of the literature assumes a single initial distribution for the agents, which limits the practical applications of MFGs.…
This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…
In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…
Policy Iteration (PI) is a classical family of algorithms to compute an optimal policy for any given Markov Decision Problem (MDP). The basic idea in PI is to begin with some initial policy and to repeatedly update the policy to one from an…
Motivated by the goal of forecasting public sentiments, we consider a forecasting problem in the context of the Mean Field Games theory. We develop a numerical method, which is a version of the so-called convexification method. We provide…
Mean-Field Games are games with a continuum of players that incorporate the time-dimension through a control-theoretic approach. Recently, simpler approaches relying on the Best Reply Strategy have been proposed. They assume that the agents…
The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP's) taking values in a general Borel space and with…
The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the retrospective analysis of a game…
We consider zero-sum stochastic games with finite state and action spaces, perfect information, mean payoff criteria, without any irreducibility assumption on the Markov chains associated to strategies (multichain games). The value of such…
We present a method enabling a large number of agents to learn how to flock, which is a natural behavior observed in large populations of animals. This problem has drawn a lot of interest but requires many structural assumptions and is…
We introduce two Smoothed Policy Iteration algorithms (\textbf{SPI}s) as rules for learning policies and methods for computing Nash equilibria in second order potential Mean Field Games (MFGs). Global convergence is proved if the coupling…
We revisit the finite time analysis of policy gradient methods in the one of the simplest settings: finite state and action MDPs with a policy class consisting of all stochastic policies and with exact gradient evaluations. There has been…
We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…
An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf…
In this paper, we consider discrete-time infinite horizon problems of optimal control to a terminal set of states. These are the problems that are often taken as the starting point for adaptive dynamic programming. Under very general…