Networked Communication for Mean-Field Games with Function Approximation and Empirical Mean-Field Estimation

Recent works have provided algorithms by which decentralised agents, which may be connected via a communication network, can learn equilibria in Mean-Field Games from a single, non-episodic run of the empirical system. However, these algorithms are given for tabular settings: this computationally limits the size of players' observation space, meaning that the algorithms are not able to handle anything but small state spaces, nor to generalise beyond policies depending on the ego player's state to so-called 'population-dependent' policies. We address this limitation by introducing function approximation to the existing setting, drawing on the Munchausen Online Mirror Descent method that has previously been employed only in finite-horizon, episodic, centralised settings. While this permits us to include the population's mean-field distribution in the observation for each player's policy, it is arguably unrealistic to assume that decentralised agents would have access to this global information: we therefore additionally provide new algorithms that allow agents to estimate the global empirical distribution based on a local neighbourhood, and to improve this estimate via communication over a given network. Our experiments showcase how the communication network allows decentralised agents to estimate the mean-field distribution for population-dependent policies, and that exchanging policy information helps networked agents to outperform both independent and even centralised agents in function-approximation settings, by an even greater margin than in tabular settings.