Recent breakthroughs in generative artificial intelligence have triggered a surge in demand for machine learning training, which poses significant cost burdens and environmental challenges due to its substantial energy consumption. Scheduling training jobs among geographically distributed cloud data centers unveils the opportunity to optimize the usage of computing capacity powered by inexpensive and low-carbon energy and address the issue of workload imbalance. To tackle the challenge of multi-objective scheduling, i.e., maximizing GPU utilization while reducing operational costs, we propose an algorithm based on multi-agent reinforcement learning and actor-critic methods to learn the optimal collaborative scheduling strategy through interacting with a cloud system built with real-life workload patterns, energy prices, and carbon intensities. Compared with other algorithms, our proposed method improves the system utility by up to 28.6% attributable to higher GPU utilization, lower energy cost, and less carbon emission.