Empirical approximation to invariant measures for McKean–Vlasov processes: Mean-field interaction vs self-interaction

Du, Kai; Jiang, Yifan; Li, Jinfeng

doi:10.3150/22-bej1550

Cited by 1 publication

(1 citation statement)

References 39 publications

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“…Along a similar direction, [Zaman et al, 2023] proposed and analyzed an RL algorithm for MFGs in a setting where the representative agent does not have access to an oracle that can provide the mean field information. Last, the question of approximating the solution to mean field dynamics using the trajectory of a single particle has been studied in [Du et al, 2023b, Du et al, 2023a, Du et al, 2023c, in the continuous space setting.…”

Section: Related Workmentioning

confidence: 99%

Unified reinforcement Q-learning for mean field game and control problems

Angiuli

Fouque

Laurière

2022

Math. Control Signals Syst.

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We establish the convergence of the unified two-timescale Reinforcement Learning (RL) algorithm presented in [Angiuli et al., 2022b]. This algorithm provides solutions to Mean Field Game (MFG) or Mean Field Control (MFC) problems depending on the ratio of two learning rates, one for the value function and the other for the mean field term. We focus a setting with finite state and action spaces, discrete time and infinite horizon. The proof of convergence relies on a generalization of the two-timescale approach of [Borkar, 1997]. The accuracy of approximation to the true solutions depends on the smoothing of the policies. We then provide an numerical example illustrating the convergence. Last, we generalize our convergence result to a three-timescale RL algorithm introduced in [Angiuli et al., 2022a] to solve mixed Mean Field Control Games (MFCGs).

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Section: Related Workmentioning

confidence: 99%