Artificial life originated and has long studied the topic of open-ended\nevolution, which seeks the principles underlying artificial systems that\ninnovate continually, inspired by biological evolution. Recently, interest has\ngrown within the broader field of AI in a generalization of open-ended\nevolution, here called open-ended search, wherein such questions of\nopen-endedness are explored for advancing AI, whatever the nature of the\nunderlying search algorithm (e.g. evolutionary or gradient-based). For example,\nopen-ended search might design new architectures for neural networks, new\nreinforcement learning algorithms, or most ambitiously, aim at designing\nartificial general intelligence. This paper proposes that open-ended evolution\nand artificial life have much to contribute towards the understanding of\nopen-ended AI, focusing here in particular on the safety of open-ended search.\nThe idea is that AI systems are increasingly applied in the real world, often\nproducing unintended harms in the process, which motivates the growing field of\nAI safety. This paper argues that open-ended AI has its own safety challenges,\nin particular, whether the creativity of open-ended systems can be productively\nand predictably controlled. This paper explains how unique safety problems\nmanifest in open-ended search, and suggests concrete contributions and research\nquestions to explore them. The hope is to inspire progress towards creative,\nuseful, and safe open-ended search algorithms.\n