title: Learning to Solve Multi-Robot Task Allocation with a Covariant-Attention based Neural Architecture
abstract: This paper demonstrates how time-constrained multi-robot task allocation (MRTA) problems can be modeled as a Markov Decision Process (MDP) over graphs, such that approximate solutions can be modeled as a policy using Reinforcement Learning (RL) methods. 
     Inspired by emerging approaches for learning to solve related combinatorial optimization (CO) problems such as multi-traveling salesman (mTSP) problems, a graph neural architecture is conceived in this paper to model the MRTA policy. The generalizability and scalability needs of the complex CO problem presented by MRTA are addressed by innovatively using the concept of Covariant Compositional Networks (CCN) to learn the local structures of graphs. The resulting learning architecture is called Covariant Attention-based Mechanism or CAM, which comprises: 1) an encoder: CCN-based embedding model to represent the task space as learnable feature vectors, 2) a decoder: an attention-based model to facilitate sequential decision outputs, and 3) context: to represent the state of the mission and the robots. To learn the feature vectors, a policy-gradient method is used. The CAM architecture is found to generally outperform a state-of-the-art encoder-decoder method that is purely based on Multi-head Attention (MHA) mechanism in terms of task completion and cost function, when applied to a class of MRTA problems with time deadlines, robot ferry range constraints, and multi-tour allowance. CAM also demonstrated significantly better scalability in terms of cost function over unseen scenarios with larger task/robot spaces than those used for training. Lastly, evidence regarding the unique potential of learning-based approaches in delivering highly time-efficient solutions is provided for a benchmark vehicle routing problem -- where solutions are achieved 100-1000 times faster compared to a non-learning baseline, and for a benchmark MRTA problem with time and capacity constraints -- where solutions for larger problems are achieved 10 times faster compared to non-learning baselines.
authors: Steve Paul Payam Ghassemi Souma Chowdhury
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