Title: Skew-Fit: State-Covering Self-Supervised Reinforcement Learning. Abstract: Autonomous agents that must exhibit flexible and broad capabilities will need to be equipped with large repertoires of skills. Defining each skill with a manually-designed reward function limits this repertoire and imposes a manual engineering burden. Self-supervised agents that set their own goals can automate this process, but designing appropriate goal setting objectives can be difficult, and often involves heuristic design decisions. In this paper, we propose a formal exploration objective for goal-reaching policies that maximizes state coverage. We show that this objective is equivalent to maximizing the entropy of the goal distribution together with goal reaching performance, where goals correspond to full state observations. To instantiate this principle, we present an algorithm called Skew-Fit for learning a maximum-entropy goal distributions. Skew-Fit enables self-supervised agents to autonomously choose and practice reaching diverse goals. We show that, under certain regularity conditions, our method converges to a uniform distribution over the set of valid states, even when we do not know this set beforehand. Our experiments show that it can learn a variety of manipulation tasks from images, including opening a door with a real robot, entirely from scratch and without any manually-designed reward function.