DAGR: State-Conditioned Goal Representations via Difference-Aware Goal Cross-Attention

This paper investigates robust representation learning in offline goal-conditioned reinforcement learning (GCRL). Particularly in sparse reward scenarios, learning representations that align state and goal latents is a challenge that frequently culminates in representation divergence where the encoder drifts toward a low-dimensional, goal-agnostic subspace that destabilizes policy learning. We address this issue by showing that an agent must acquire a fundamental understanding of its environment across multiple scales, from local physical dynamics to long-horizon goal-directed structure. Building on this insight, we propose Ms.PR, a framework that leverages multi-scale predictive supervision to enforce goal-directed alignment within the latent space. We demonstrate that Ms.PR leads to improved representation quality and strong performance on both vision and state-based tasks. Furthermore, we show that our approach is exceptionally resilient under realistic, challenging data regimes, maintaining state-of-the-art performance across a wide variety of tasks, trajectory stitching scenarios, and extreme noise conditions.

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.

Offline goal-conditioned reinforcement learning requires both long-horizon reachability estimates and local action comparisons. Dual goal representations provide value fields that capture global goal reachability, but they do not directly specify which action should be preferred at a given state. We propose Dual Advantage Fields, a policy-extraction method that turns a bilinear dual value model into a local advantage signal. Under bilinear dual parameterization, the goal embedding is the gradient of the value field with respect to the state representation. DAF learns an action-effect model that predicts the discounted feature displacement induced by an action and scores actions by the alignment between this displacement and the goal direction. In the realizable case, this score equals the goal-conditioned Bellman advantage, yielding a standard local policy-improvement guarantee. On OGBench locomotion, manipulation, and puzzle tasks, DAF improves aggregate RLiable metrics and performs strongly in settings where locally correct actions differ from direct movement toward the final goal.