  In many domains such as transportation and logistics, search and rescue, or
cooperative surveillance, tasks are pending to be allocated with the
consideration of possible execution uncertainties. Existing task coordination
algorithms either ignore the stochastic process or suffer from the
computational intensity. Taking advantage of the weakly coupled feature of the
problem and the opportunity for coordination in advance, we propose a
decentralized auction-based coordination strategy using a newly formulated
score function which is generated by forming the problem into task-constrained
Markov decision processes (MDPs). The proposed method guarantees convergence
and at least 50% optimality in the premise of a submodular reward function.
Furthermore, for the implementation on large-scale applications, an approximate
variant of the proposed method, namely Deep Auction, is also suggested with the
use of neural networks, which is evasive of the troublesome for constructing
MDPs. Inspired by the well-known actor-critic architecture, two Transformers
are used to map observations to action probabilities and cumulative rewards
respectively. Finally, we demonstrate the performance of the two proposed
approaches in the context of drone deliveries, where the stochastic planning
for the drone league is cast into a stochastic price-collecting Vehicle Routing
Problem (VRP) with time windows. Simulation results are compared with
state-of-the-art methods in terms of solution quality, planning efficiency and
scalability.
