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Cross-domain imitation learning studies how to leverage expert demonstrations of one agent to train an imitation agent with a different embodiment or morphology. Comparing trajectories and stationary distributions between the expert and imitation agents is challenging because they live on different systems that may not even have the same dimensionality. We propose Gromov-Wasserstein Imitation Learning (GWIL), a method for cross-domain imitation that uses the Gromov-Wasserstein distance to align and compare states between the different spaces of the agents. Our theory formally characterizes the scenarios where GWIL preserves optimality, revealing its possibilities and limitations. We demonstrate the effectiveness of GWIL in non-trivial continuous control domains ranging from simple rigid transformation of the expert domain to arbitrary transformation of the state-action space. 1

Reinforcement learning (RL) provides a framework for learning goal-directed policies given user-specified rewards. However, since designing rewards often requires substantial engineering effort, we are interested in the problem of learning without rewards, where agents must discover useful behaviors in the absence of task-specific incentives. Intrinsic motivation is a family of unsupervised RL techniques which develop general objectives for an RL agent to optimize that lead to better exploration or the discovery of skills. In this paper, we propose a new unsupervised RL technique based on an adversarial game which pits two policies against each other to compete over the amount of surprise an RL agent experiences. The policies each take turns controlling the agent. The Explore policy maximizes entropy, putting the agent into surprising or unfamiliar situations. Then, the Control policy takes over and seeks to recover from those situations by minimizing entropy. The game harnesses the power of multi-agent competition to drive the agent to seek out increasingly surprising parts of the environment while learning to gain mastery over them. We show empirically that our method leads to the emergence of complex skills by exhibiting clear phase transitions. Furthermore, we show both theoretically -via a latent state space coverage argument-and empirically that our method has the potential to be applied to the exploration of stochastic, partiallyobserved environments. We show that Adversarial Surprise learns more complex behaviors, and explores more effectively than competitive baselines, outperforming intrinsic motivation methods based on active inference, novelty-seeking (Random Network Distillation (RND)), and multi-agent unsupervised RL (Asymmetric Self-Play (ASP)) in MiniGrid, Atari and VizDoom environments. * Equal contribution.Preprint. Under review.

We introduce the concept of a multi-principal assistance game (MPAG), and circumvent an obstacle in social choice theory -Gibbard's theorem -by using a sufficiently "collegial" preference inference mechanism. In an MPAG, a single agent assists N human principals who may have widely different preferences. MPAGs generalize assistance games, also known as cooperative inverse reinforcement learning games. We analyze in particular a generalization of apprenticeship learning in which the humans first perform some work to obtain utility and demonstrate their preferences, and then the robot acts to further maximize the sum of human payoffs. We show in this setting that if the game is sufficiently collegial -i.e., if the humans are responsible for obtaining a sufficient fraction of the rewards through their own actions -then their preferences are straightforwardly revealed through their work. This revelation mechanism is non-dictatorial, does not limit the possible outcomes to two alternatives, and is dominant-strategy incentive-compatible.