Bottleneck-Guided Spectral Subgoals For Offline Goal-Conditioned RL

Offline goal-conditioned RL (OGCRL) learns to reach arbitrary goals from the offline dataset, but long-horizon performance hinges on crossing a handful of hard-to-cross bottlenecks. These bottlenecks not only dictate the feasible paths toward the goal but also act as critical keypoints, marking the transitions between adjacent regions and providing the agent with essential directional guidance. Prior hierarchical methods pick subgoals by time or short-horizon value heuristics, which do not localize the bottleneck, and therefore the agent loses the clear guidance that bottlenecks could provide about where to pass next. We instead model long-horizon planning as ``cross the next bottleneck'': we apply Laplacian spectral clustering to the offline dataset to expose bottlenecks, identify trajectories from the offline dataset that cross these boundaries, and use the corresponding boundary-supported states as keypoint (KP) candidates. The most representative KPs are then instantiated from these candidates, and a directed KP reachability graph $\mathcal G_{\mathrm{KP}}$ is constructed based on the resulting KPs. We then restrict high-level choices to these bottleneck states and use a pluggable low-level controller to execute the short transitions between them. We provide theory showing that under a standard metastable decomposition of the state space, routing through bottlenecks yields an (approximately) optimal one-step subgoal in terms of hitting-time, and that Laplacian spectra recover bottlenecks with high overlap. Thus, Laplacian spectral clustering can discover near-optimal subgoals under these assumptions. Empirically, the same pattern holds: across D4RL and OGBench, our method achieves state-of-the-art results on a broad set of navigation and manipulation tasks and across diverse dataset regimes, for example, 96.5% on AntMaze and 84.7% on Franka-Kitchen.