Title: Learning to Solve Multi-Robot Task Allocation with a Covariant-Attention based Neural Architecture. Abstract: This paper presents a new graph neural network architecture over which reinforcement learning can be performed to yield online policies for an important class of multi-robot task allocation (MRTA) problems, one that involves tasks with deadlines, and robots with ferry range and payload constraints and multi-tour capability. While drawing motivation from recent graph learning methods that learn to solve combinatorial optimization problems of the mTSP/VRP type, this paper seeks to provide better convergence and generalizability specifically for MRTA problems. The proposed neural architecture, called Covariant Attention-based Model or CAM, includes three main components: 1) an encoder: a covariant compositional node-based embedding is used to represent each task as a learnable feature vector in manner that preserves the local structure of the task graph while being invariant to the ordering of graph nodes; 2) context: a vector representation of the mission time and state of the concerned robot and its peers; and 2) a decoder: builds upon the attention mechanism to facilitate a sequential output. In order to train the CAM model, a policy-gradient method based on REINFORCE is used. While the new architecture can solve the broad class of MRTA problems stated above, to demonstrate real-world applicability we use a multi-unmanned aerial vehicle or multi-UAV-based flood response problem for evaluation purposes. For comparison, the well-known attention-based approach (designed to solve mTSP/VRP problems) is extended and applied to the MRTA problem, as a baseline. The results show that the proposed CAM method is not only superior to the baseline AM method in terms of the cost function (over training and unseen test scenarios), but also provide significantly faster convergence and yields learnt policies that can be executed within 2.4ms/robot, thereby allowing real-time application.