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In this paper we explore the theoretical boundaries of planning in a settingwhere no model of the agent's actions is given. Instead of an action model, aset of successfully executed plans are given and the task is to generate a planthat is safe, i.e., guaranteed to achieve the goal without failing. To thisend, we show how to learn a conservative model of the world in which actionsare guaranteed to be applicable. This conservative model is then given to anoff-the-shelf classical planner, resulting in a plan that is guaranteed toachieve the goal. However, this reduction from a model-free planning to amodel-based planning is not complete: in some cases a plan will not be foundeven when such exists. We analyze the relation between the number of observedplans and the likelihood that our conservative approach will indeed fail tosolve a solvable problem. Our analysis show that the number of trajectoriesneeded scales gracefully.

Efficient, Safe, and Probably Approximately Complete Learning of Action Models