Theyanesh Eswaramoorthy Rajahkrishnan

arXiv2026

Direction-Conditioned Policies for Online Goal-Conditioned Reinforcement Learning

Contrastive Reinforcement Learning (CRL) learns representations that estimate goal reachability, yet its policy remains conditioned on raw goals and therefore does not directly exploit the geometry encoded by its critic. We introduce Direction-Conditioned Policies (DCP), a method built around a small modification to CRL: DCP selects previously visited states as waypoints during online training and conditions the policy on their direction and distance in representation space. At deployment, DCP applies the same interface directly to the final goal, requiring neither waypoint selection nor planning. Across nine navigation and manipulation tasks, DCP attains higher final success rates than CRL on seven tasks and spends more time near the goal on seven. Controlled maze experiments further show that DCP captures shortest-path geometry more accurately and that the supplied direction causally influences the actor's behavior. We identify waypoint coverage and ranking as limits to exploration, and show that learned candidate generation improves goal reaching in two controlled mazes.

cs.LG↗

arXiv2026

Direction-Conditioned Policies via Compositional Subgoal Scoring for Online Goal-Conditioned Reinforcement Learning

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 $z_t$ aligned with the final goal $g$ in $ψ_g$, and a direction-conditioned actor that consumes the unit direction $d_t$ and magnitude $r_t$ from $ψ(s_t)$ to $ψ(z_t)$. The two components train jointly, factor cleanly at deployment (subgoal scoring is removed, while direction conditioning remains with $g$ in place of $z_t$), and admit independent modification at the same $(d_t,r_t)$ 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 $z_t$, 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.

cs.LG↗