Under uniform ergodicity and Lipschitz assumptions, the rescaled parameter process of multi-agent RL learners in a finite-state Markov game converges weakly to the ODE that averages each update against the stationary distribution of the fast game state.
Geometric fluid approximation for general continuous-time markov chains
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Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games
Under uniform ergodicity and Lipschitz assumptions, the rescaled parameter process of multi-agent RL learners in a finite-state Markov game converges weakly to the ODE that averages each update against the stationary distribution of the fast game state.