Entropy-Regularized Mean-Field Games with Average-Reward Criterion: Span-Seminorm Contractions and Model-Free Learning
The paper investigates entropy-regularized mean-field games under an average-reward criterion to find a unique equilibrium. It introduces a soft Q-operator that acts as a span-seminorm contraction, allowing relative value iteration to solve the optimality equation. Furthermore, it develops a model-free learning algorithm that converges to this equilibrium using sample-based updates for both the Q-operator and population distribution.