skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Learning Deep Mean Field Games for Modeling Large Population Behavior
We consider the problem of representing collective behavior of large popula- tions and predicting the evolution of a population distribution over a discrete state space. A discrete time mean field game (MFG) is motivated as an interpretable model founded on game theory for understanding the aggregate effect of individ- ual actions and predicting the temporal evolution of population distributions. We achieve a synthesis of MFG and Markov decision processes (MDP) by showing that a special MFG is reducible to an MDP. This enables us to broaden the scope of mean field game theory and infer MFG models of large real-world systems via deep inverse reinforcement learning. Our method learns both the reward function and forward dynamics of an MFG from real data, and we report the first empirical test of a mean field game model of a real-world social media population.  more » « less
Award ID(s):
1745382 1620342
PAR ID:
10112528
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
International Conference on Learning Representations (ICLR)
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; (, IEEE Conference on Computer Communications INFOCOM)
    null (Ed.)
    We consider an ultra-dense wireless network with N channels and M = N devices. Messages with fresh information are generated at each device according to a random process and need to be transmitted to an access point. The value of a message decreases as it ages, so each device searches for an idle channel to transmit the message as soon as it can. However, each channel probing is associated with a fixed cost (energy), so a device needs to adapt its probing rate based on the "age" of the message. At each device, the design of the optimal probing strategy can be formulated as an infinite horizon Markov Decision Process (MDP) where the devices compete with each other to find idle channels. While it is natural to view the system as a Bayesian game, it is often intractable to analyze such a system. Thus, we use the Mean Field Game (MFG) approach to analyze the system in a large-system regime, where the number of devices is very large, to understand the structure of the problem and to find efficient probing strategies. We present an analysis based on the MFG perspective. We begin by characterizing the space of valid policies and use this to show the existence of a Mean Field Nash Equilibrium (MFNE) in a constrained set for any general increasing cost functions with diminishing rewards. Further we provide an algorithm for computing the equilibrium for any given device, and the corresponding age-dependent channel probing policy. 
    more » « less
  2. ; ; (, Mathematics)
    This paper proposes a scalable learning framework to solve a system of coupled forward–backward partial differential equations (PDEs) arising from mean field games (MFGs). The MFG system incorporates a forward PDE to model the propagation of population dynamics and a backward PDE for a representative agent’s optimal control. Existing work mainly focus on solving the mean field game equilibrium (MFE) of the MFG system when given fixed boundary conditions, including the initial population state and terminal cost. To obtain MFE efficiently, particularly when the initial population density and terminal cost vary, we utilize a physics-informed neural operator (PINO) to tackle the forward–backward PDEs. A learning algorithm is devised and its performance is evaluated on one application domain, which is the autonomous driving velocity control. Numerical experiments show that our method can obtain the MFE accurately when given different initial distributions of vehicles. The PINO exhibits both memory efficiency and generalization capabilities compared to physics-informed neural networks (PINNs). 
    more » « less
  3. ; ; ; (, Proceedings of Machine Learning Research)
    null (Ed.)
    Mean Field Games (MFG) are the class of games with a very large number of agents and the standard equilibrium concept is a Mean Field Equilibrium (MFE). Algorithms for learning MFE in dynamic MFGs are un- known in general. Our focus is on an important subclass that possess a monotonicity property called Strategic Complementarities (MFG-SC). We introduce a natural refinement to the equilibrium concept that we call Trembling-Hand-Perfect MFE (T-MFE), which allows agents to employ a measure of randomization while accounting for the impact of such randomization on their payoffs. We propose a simple algorithm for computing T-MFE under a known model. We also introduce a model-free and a model-based approach to learning T-MFE and provide sample complexities of both algorithms. We also develop a fully online learning scheme that obviates the need for a simulator. Finally, we empirically evaluate the performance of the proposed algorithms via examples motivated by real-world applications. 
    more » « less
  4. ; ; ; (, Proceedings of Machine Learning Research)
    null (Ed.)
    Mean Field Games (MFG) are the class of games with a very large number of agents and the standard equilibrium concept is a Mean Field Equilibrium (MFE). Algorithms for learning MFE in dynamic MFGs are unknown in general. Our focus is on an important subclass that possess a monotonicity property called Strategic Complementarities (MFG-SC). We introduce a natural refinement to the equilibrium concept that we call Trembling-Hand-Perfect MFE (T-MFE), which allows agents to employ a measure of randomization while accounting for the impact of such randomization on their payoffs. We propose a simple algorithm for computing T-MFE under a known model. We also introduce a model-free and a model-based approach to learning T-MFE and provide sample complexities of both algorithms. We also develop a fully online learning scheme that obviates the need for a simulator. Finally, we empirically evaluate the performance of the proposed algorithms via examples motivated by real-world applications. 
    more » « less
  5. ; (, Dynamic Games and Applications)
    We consider a class of deterministic mean field games, where the state associated with each player evolves according to an ODE which is linear w.r.t. the control. Existence, uniqueness, and stability of solutions are studied from the point of viewof generic theory. Within a suitable topological space of dynamics and cost functionals, we prove that, for “nearly all” mean field games (in the Baire category sense) the best reply map is single-valued for a.e. player. As a consequence, the mean field game admits a strong (not randomized) solution. Examples are given of open sets of games admitting a single solution, and other open sets admitting multiple solutions. Further examples show the existence of an open set of MFG having a unique solution which is asymptotically stable w.r.t. the best reply map, and another open set of MFG having a unique solution which is unstable. We conclude with an example of a MFG with terminal constraints which does not have any solution, not even in the mild sense with randomized strategies. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email