  Order execution is a fundamental task in quantitative finance, aiming at
finishing acquisition or liquidation for a number of trading orders of the
specific assets. Recent advance in model-free reinforcement learning (RL)
provides a data-driven solution to the order execution problem. However, the
existing works always optimize execution for an individual order, overlooking
the practice that multiple orders are specified to execute simultaneously,
resulting in suboptimality and bias. In this paper, we first present a
multi-agent RL (MARL) method for multi-order execution considering practical
constraints. Specifically, we treat every agent as an individual operator to
trade one specific order, while keeping communicating with each other and
collaborating for maximizing the overall profits. Nevertheless, the existing
MARL algorithms often incorporate communication among agents by exchanging only
the information of their partial observations, which is inefficient in
complicated financial market. To improve collaboration, we then propose a
learnable multi-round communication protocol, for the agents communicating the
intended actions with each other and refining accordingly. It is optimized
through a novel action value attribution method which is provably consistent
with the original learning objective yet more efficient. The experiments on the
data from two real-world markets have illustrated superior performance with
significantly better collaboration effectiveness achieved by our method.
