In multi-task reinforcement learning, it is possible to improve the data efficiency of training agents by transferring knowledge from other different but related tasks. Because the experiences from different tasks are usually biased toward the specific task goals. Traditional methods rely on Kullback-Leibler regularization to stabilize the transfer of knowledge from one task to the others. In this work, we explore the direction of replacing the Kullback-Leibler divergence with a novel Optimal transport-based regularization. By using the Sinkhorn mapping, we can approximate the Optimal transport distance between the state distribution of tasks. The distance is then used as an amortized reward to regularize the amount of sharing information. We experiment our frameworks on several grid-based navigation multi-goal to validate the effectiveness of the approach. The results show that our added Optimal transport-based rewards are able to speed up the learning process of agents and outperforms several baselines on multi-task learning.

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