Addressing hard constraints in the air traffic problem through partitioning and difference rewards

In the US alone, weather hazards and airport congestion cause thousands of hours of delay, costing billions of dollars annually. The task of managing delay may be modeled as a multiagent congestion problem with tightly coupled agents who collectively impact the system. Reward shaping has been effective at reducing noise caused by agent interaction and improving learning in soft constraint problems. We ex-tend those results to hard constraints that cannot be easily learned, and must be algorithmically enforced. We present an agent partitioning algorithm in conjunction with reward shaping to simplify the learning domain. Our results show that a partitioning of the agents using system features leads to up to a 1000x speed up over the straight reward shaping approach, as well as up to a 30 % improvement in perfor-mance over a greedy scheduling solution, corresponding to hundreds of hours of delay saved in a single day