The authors propose actor-critic q-learning algorithms for mean-field control with common noise based on martingale orthogonality conditions and relaxed controls, establish convergence of inner iterations in the linear-quadratic case, and demonstrate performance on examples.
Lions (2006): Cours au coll\` e ge de france: Th\' e orie des jeux \` a champ moyens
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Continuous-time q-learning for mean-field control with common noise, part-II: q-learning algorithms
The authors propose actor-critic q-learning algorithms for mean-field control with common noise based on martingale orthogonality conditions and relaxed controls, establish convergence of inner iterations in the linear-quadratic case, and demonstrate performance on examples.