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Neural networks have shown state-of-the-art performance in designingauctions, where the network learns the optimal allocations and payment rule toensure desirable properties. Motivated by the same, we focus on learning fairdivision of resources, with no payments involved. Our goal is to allocate theitems, goods and/or chores efficiently among the fair allocations. By fair, wemean an allocation that is Envy-free (EF). However, such an allocation may notalways exist for indivisible resources. Therefore, we consider the relaxednotion, Envy-freeness up to one item (EF1) that is guaranteed to exist.However, it is not enough to guarantee EF1 since the allocation of emptybundles is also EF1. Hence, we add the further constraint of efficiency,maximum utilitarian social welfare (USW). In general finding, USW allocationsamong EF1 is an NP-Hard problem even when valuations are additive. In thiswork, we design a network for this task which we refer to as EEF1-NN. Wepropose an UNet inspired architecture, Lagrangian loss function, and trainingprocedure to obtain desired results. We show that EEF1-NN finds allocationclose to optimal USW allocation and ensures EF1 with a high probability fordifferent distributions over input valuations. Compared to existing approachesEEF1-NN empirically guarantees higher USW. Moreover, EEF1-NN is scalable anddetermines the allocations much faster than solving it as a constrainedoptimization problem.

EEF1-NN: Efficient and EF1 allocations through Neural Networks