Recent algorithmic and theoretical advances in reinforcement learning (RL) have attracted widespread interest. RL algorithms have appeared that approximate dynamic programming on an incremental basis. They can be trained on the basis of real or simulated experiences, focusing their computation on areas of state space that are actually visited during control, making them computationally tractable on very large problems. If each member of a team of agents employs one of these algorithms, a new collective learning algorithm emerges for the team as a whole. In this paper we demonstrate that such collective RL algorithms can be powerful heuristic methods for addressing large-scale control problems. Elevator group control serves as our testbed. It is a difficult domain posing a combination of challenges not seen in most multi-agent learning research to date. We use a team of RL agents, each of which is responsible for controlling one elevator car. The team receives a global reward signal which appears noisy to each agent due to the effects of the actions of the other agents, the random nature of the arrivals and the incomplete observation of the state. In spite of these complications, we show results that in simulation surpass the best of the heuristic elevator control algorithms of which we are aware. These results demonstrate the power of multi-agent RL on a very large scale stochastic dynamic optimization problem of practical utility.