Learning Goal-Reaching Quasimetric Geometry From Finite-Time Reachability

Offline goal-conditioned reinforcement learning (GCRL) is typically benchmarked by the best tuned success rate of each method. This score measures attainable performance, but it does not reveal how reliably a learned goal-conditioned signal can be extracted into a policy: a method could succeed across many value-learning and extraction settings, or only at a narrow, hard-to-find configuration. We study this gap across four methods, GCIQL, GCIVL, QRL, and CRL, under a shared advantage-weighted regression (AWR) extractor. For each method, we construct trainability landscapes over the optimizer learning rate, which affects value learning and actor optimization, and AWR temperature, which controls how selectively the actor imitates high-advantage transitions. Across AntMaze, Cube, and Scene, we observe distinct regimes: high-scoring methods may be broadly accessible or brittle, while broad relative basins may still sit below low absolute ceilings. To interpret these differences, we pair landscapes with post-hoc diagnostics of future-vs-random goal discrimination and AWR weight concentration. Their relationship to downstream success is task-dependent. On AntMaze, where future goals align with path-like progress, these diagnostics explain landscape regimes. On Cube and Scene, goal ranking and manipulation control decouple: methods can rank goals well while failing downstream, or succeed through action-conditioned advantages despite weak future-vs-random separation. These results show that peak tuned success alone does not establish broadly extractable goal-conditioned behavior. Trainability landscapes expose this gap, while extraction diagnostics offer a lower-cost lens on how learned signals become policies.

Offline goal-conditioned reinforcement learning (GCRL) is challenging in long-horizon tasks, where distant state--goal pairs provide weak supervision and value estimates become vulnerable to accumulated bootstrapping errors. Hierarchical methods mitigate this difficulty by introducing intermediate subgoals, but fixed temporal abstractions or fixed hierarchy depths can be mismatched to state--goal pairs with different reachability horizons. We propose Coarse-to-Fine Hierarchical Goal Reinforcement Learning (CFHRL), a fully offline GCRL framework that adaptively refines distant goals before execution. Starting from the final goal, CFHRL recursively proposes intermediate targets, trained from replay-supported candidates, and stops refinement once the current target is estimated to be locally executable by a learned reachability cost. The key idea is that a subgoal need not be an exact midpoint or globally optimal waypoint; it only needs to provide reliable progress and reduce the remaining reaching difficulty, enabling subsequent refinement over shorter horizons. A stylized analysis further supports the robustness of approximate recursive contraction. Experiments on OGBench show substantial gains on several long-horizon tasks, with ablations validating the proposed refinement and stopping mechanisms

Goal-conditioned reinforcement learning (GCRL) relies heavily on how target goals are represented to the policy. While recent methods encode goals via temporal distance, occupancy, or controllability, it remains unclear how much downstream performance actually depends on representation quality. We study this in offline GCRL by constructing an exact temporal-distance goal representation in deterministic mazes. We then systematically corrupt its geometric quality while keeping the downstream learner fixed. Across OGBench navigation tasks and two algorithms, large changes in goal-representation quality produce almost no change in performance. However, applying the same interventions to the agent's current state more than doubles success, revealing the state pathway as the true bottleneck. Building on this insight, we show that simple random Fourier positional encodings substantially improve performance on the hardest navigation tasks without map information or objective modifications. Overall, our findings suggest that in state-based offline navigation, improving how the agent's current state is represented matters far more than refining the goal representation. Code will be released soon.