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In this paper, we revisit endless online level generation with the recentlyproposed experience-driven procedural content generation via reinforcementlearning (EDRL) framework. Inspired by an observation that EDRL tends togenerate recurrent patterns, we formulate a notion of state space closure whichmakes any stochastic state appeared possibly in an infinite-horizon onlinegeneration process can be found within a finite-horizon. Through theoreticalanalysis, we find that even though state space closure arises a concern aboutdiversity, it generalises EDRL trained with a finite-horizon to theinfinite-horizon scenario without deterioration of content quality. Moreover,we verify the quality and the diversity of contents generated by EDRL viaempirical studies, on the widely used Super Mario Bros. benchmark. Experimentalresults reveal that the diversity of levels generated by EDRL is limited due tothe state space closure, whereas their quality does not deteriorate in ahorizon which is longer than the one specified in the training. Concluding ouroutcomes and analysis, future work on endless online level generation viareinforcement learning should address the issue of diversity while assuring theoccurrence of state space closure and quality.

State Space Closure: Revisiting Endless Online Level Generation via Reinforcement Learning