bottleneck states

Some states are pinch points: nearly every path from one region of the world to another has to squeeze through them. A doorway between two rooms is the classic picture — whatever you are doing on this side, if you want to be on the other side you must pass through that door. Bottleneck states are exactly these pivotal waypoints, and they are prime candidates for subgoals because reaching one unlocks a whole new part of the space.

Algorithms find them by looking at the connectivity of the state space. Some build a graph of transitions and compute betweenness centrality, flagging states that lie on a disproportionate share of shortest paths. Others notice states that appear on many successful trajectories but seldom otherwise, or use spectral methods on the transition graph to spot natural partitions whose boundaries are the bottlenecks. Once identified, an option or goal is created to reliably drive the agent to each one.

Why bother? Because a bottleneck subgoal cleaves a hard long-horizon problem into easier pieces: learn to reach the doorway, then learn what to do beyond it, instead of solving the whole maze at once. The caveat is that bottlenecks are easy to define in tidy navigation worlds but slippery in high-dimensional or continuous tasks, where 'the doorway' may have no crisp counterpart.