Efficient exploration under sparse rewards remains a key challenge in deep reinforcement learning. To guide exploration, previous work makes extensive use of intrinsic reward (IR). There are many heuristics for IR, including visitation counts, curiosity, and state-difference. In this paper, we analyze the pros and cons of each method and propose the regulated difference of inverse visitation counts as a simple but effective criterion for IR. The criterion helps the agent explore Beyond the Boundary of explored regions and mitigates common issues in count-based methods, such as short-sightedness and detachment. The resulting method, BeBold, solves the 12 most challenging procedurally-generated tasks in MiniGrid with just 120M environment steps, without any curriculum learning. In comparison, the previous SoTA only solves 50% of the tasks. BeBold also achieves SoTA on multiple tasks in NetHack, a popular rogue-like game that contains more challenging procedurally-generated environments.
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