Dual Advantage Fields

Goal-conditioned reinforcement learning hinges on how the goal is encoded. Contrastive, metric, temporal-distance, and information-theoretic encoders differ in objective. They still share one trait. None of them sees the current state. Such a state-independent embedding cannot mark which part of the goal still needs action. The policy must then recover that cue by inverting both encoders. We propose DAGR. It refines the static embedding of any late-fusion encoder into a state-conditioned one through multi-scale gated cross-attention. A near-identity gated residual preserves the base representation. Difference-aware Goal Cross-Attention then biases the attention scores using a per-token state-goal discrepancy map. On OGBench, DAGR improves navigation. Our ablations trace the gain to the gated residual, not to the difference bias that names the method. On manipulation and puzzle tasks it matches or falls below the base. DAGR is a structured refinement, not a universal improvement.

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 (GCRL) provides a practical framework for obtaining goal-reaching policies from fixed datasets. However, learning a reliable goal-conditioned value function in long-horizon tasks remains challenging. In this paper, we identify erroneous generalization in goal-conditioned value functions as a fundamental bottleneck, and demonstrate that appropriate inductive bias in the value function is crucial for addressing the bottleneck. Building on these findings, we propose Latent-Aligned Value Learning (LAVL), an offline GCRL algorithm that integrates latent-representation-based value generalization with hierarchical planning in a unified framework. Extensive experiments on OGBench demonstrate that LAVL consistently outperforms existing offline GCRL methods, achieving the highest performance on 20 out of 22 datasets. Notably, LAVL exhibits strong performance in long-horizon tasks and trajectory stitching datasets, where prior methods suffer significant performance degradation. Our code is available at https://github.com/oh-lab/LAVL.git.