Poor sample efficiency is a major limitation of deep reinforcement learning in many domains. This work presents an attention-based method to project neural network inputs into an efficient representation space that is invariant under changes to input ordering. We show that our proposed representation results in an input space that is a factor of $m!$ smaller for inputs of $m$ objects. We also show that our method is able to represent inputs over variable numbers of objects. Our experiments demonstrate improvements in sample efficiency for policy gradient methods on a variety of tasks. We show that our representation allows us to solve problems that are otherwise intractable when using naive approaches.
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