Hamilton-Jacobi-Bellman theory implies that the optimal goal-conditioned action depends on the goal only through the gradient of the goal-reaching distance at the current state, yet standard online GCRL still conditions the actor on the raw goal -- a signal that is geometrically uninformative when the goal is far from the data distribution. We propose Direction-Conditioned Policies (DCP), a fully online method that decomposes goal-reaching into two components sharing one InfoNCE representation ψ: a subgoal-scoring step that selects a visited state zt aligned with the final goal g in ψg, and a direction-conditioned actor that consumes the unit direction dt and magnitude rt from ψ(st) to ψ(zt). The two components train jointly, factor cleanly at deployment (subgoal scoring is removed, while direction conditioning remains with g in place of zt), and admit independent modification at the same (dt,rt) interface. We prove three results. First, direction sufficiency under HJB: the optimal action under control-affine dynamics depends on the goal only through the value gradient. Second, a quantitative bound showing that, under mild conditions on the learned representation and assuming the scoring rule returns an on-path zt, the actor's conditioning input at training and at deployment coincide up to representation error and geodesic slack. Third, a controllable-subspace characterization of when directional conditioning fails. Across nine environments, DCP improves over Contrastive RL on most final metrics, with the largest gains on manipulation and obstacle-interaction tasks; a qualitative analysis of the learned ψ-distance landscape shows the contrastive representation behaves as an online quasimetric encoding environment topology, and the single failure case (AntSoccer) localizes to a learned-gradient pathology that the theory anticipates.
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 aims to learn policies that reach specified goals, but remains challenging in offline settings with sparse rewards and long-horizon dependencies. In such settings, goal-completion information can be temporally distant from the early decisions that enable success, while offline value estimation introduces additional error. We study this issue from a reward-propagation perspective and show, in a stylized delayed-goal setting, how goal-directed value separation can become small relative to local estimation error. Motivated by this analysis, we propose Reward Stimulation Implicit Q-Learning (RSIQL), a simple non-hierarchical method that introduces additional reward signals at progress-making intermediate states in offline trajectories. RSIQL uses an auxiliary goal-conditioned value function to identify intermediate states estimated to make progress toward the goal and applies reward stimulation to provide less-delayed training supervision. Unlike hierarchical methods, RSIQL does not learn a separate high-level subgoal policy. Experiments on D4RL goal-reaching benchmarks and OGBench show that RSIQL improves over goal-conditioned IQL on average and achieves performance competitive with hierarchical offline goal-conditioned methods, while retaining a simple flat policy structure.
Goal-conditioned reinforcement learning struggles with long horizons when rewards are sparse. While a planner can provide subgoals to guide a low-level policy, its use at test time may introduce practical subgoal management difficulties. An alternative paradigm utilizes a high-level planner to assist learning, while the policy remains conditioned only on the final goal, enabling planner-free deployment. Among these methods, Reinforcement Learning with Imagined Subgoals (RIS) introduces a regularization term that encourages the policy to take the same actions for the final goal as it does for an intermediate goal. This regularization, however, may lead to goal-chaining issues when intermediate goals are low-dimensional. Potential-based reward shaping (PBRS) translates plans into an additional reward while ensuring that the optimal policy remains unchanged. Yet, it can generate deceptive rewards in terminal states. We study these failure cases and first propose an alternative reward shaping method (RS) that removes these deceptive rewards at the expense of theoretical guarantees of PBRS. Similar to this RS variant, we then propose another method named Locally-Guided Actor Critic (LG-AC) that rewards the agent for reaching intermediate goals. Unlike RS, where intermediate rewards are implicit in the shaping signal, we explicitly condition a value estimator on the full sequence of intermediate goals but represent the value function as a sum of subgoal-conditioned value functions, enabling dense hindsight relabeling. We evaluate all these methods in tasks with challenging goal-chaining requirements and empirically highlight specific cases in which either action regularization or reward shaping yield low performance, while LG-AC achieves the best overall performance across tasks.