This paper addresses the important challenge of obtaining a planning model that accurately represents the problem dynamics in applying planning techniques to real-world problems. This is especially difficult in mission-critical domains where trial-and-error learning is impossible. Therefore, the action model used for planning must be safe, and the generated plan must be applicable and achieve the goal. Previous studies have mainly studied safe action model learning in domains where states can be sufficiently described by Boolean variables. In this paper, we propose a numerically safe action model learning (N-SAM) algorithm that overcomes these limitations and can learn safe numerical antecedents and effects. N-SAM runs in linear time with respect to the number of observations and is guaranteed to return safe action models under certain conditions. However, in order to maintain this safety guarantee, a significant number of examples of each action must be observed before including the action in the learned model. To address this limitation of N-SAM, this paper proposes an N-SAM* algorithm that ensures that each observed action is applicable in at least some states. N-SAM includes actions that are observed only once and does not compromise safety. N-SAM is proven to be optimal in terms of sample complexity compared to other algorithms that guarantee safety. N-SAM and N-SAM* are evaluated on a wide range of numerical programming domain benchmarks and compared to state-of-the-art numerical action model learning algorithms. In addition, we provide a discussion on the impact of numerical accuracy on the learning process.
