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But yet there is no coherent definition of open-endedness or theory about how an agent ought to explore an open-ended environment. We introduce an information-theoretic definition based on a new concept -- the ${\\textit bit-equivalent}$ -- which quantifies the information required to attain each level of expected reward. We consider an environment to be open-ended if an agent can attain linear growth in the bit-equivalent. We establish that classical bandit environments are not open-ended and formulate a bandit environment that is. We also introduce an algorithm that achieves open-ended learning in this environment.","title":"An Information-Theoretic Definition for Open-Ended Learning","url":"https://arxiv.org/abs/2606.08369","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.08369v1 Announce Type: cross \nAbstract: A growing body of work points to the great promise of AI systems that can continually expand their capabilities as they operate in an open-ended environment. 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