Serverless Function-as-a-Service (FaaS) offers improved programmability for customers, yet it is not server-“less” and comes at the cost of more complex infrastructure management (e.g., resource provisioning and scheduling) for cloud providers. To maintain service-level objectives (SLOs) and improve resource utilization efficiency, recent research has been focused on applying online learning algorithms such as reinforcement learning (RL) to manage resources. Despite the initial success of applying RL, we first show in this paper that the state-of-the-art single-agent RL algorithm (S-RL) suffers up to 4.8× higher p99 function latency degradation on multi-tenant serverless FaaS platforms compared to isolated environments and is unable to converge during training. We then design and implement a scalable and incremental multi-agent RL framework based on Proximal Policy Optimization (SIMPPO). Our experiments demonstrate that in multi-tenant environments, SIMPPO enables each RL agent to efficiently converge during training and provides online function latency performance comparable to that of S-RL trained in isolation with minor degradation (<9.2%). In addition, SIMPPO reduces the p99 function latency by 4.5× compared to S-RL in multi-tenant cases.