In this paper, we propose multi-agent automated machine learning (MA2ML) with the aim to effectively handle joint optimization of modules in automated machine learning (AutoML). MA2ML takes each machine learning module, such as data augmentation (AUG), neural architecture search (NAS), or hyper-parameters (HPO), as an agent and the final performance as the reward, to formulate a multi-agent reinforcement learning problem. MA2ML explicitly assigns credit to each agent according to its marginal contribution to enhance cooperation among modules, and incorporates off-policy learning to improve search efficiency. Theoretically, MA2ML guarantees monotonic improvement of joint optimization. Extensive experiments show that MA2ML yields the state-of-the-art top-1 accuracy on ImageNet under constraints of computational cost, e.g., 79.7%/80.5% with FLOPs fewer than 600M/800M. Extensive ablation studies verify the benefits of credit assignment and off-policy learning of MA2ML.