Geometry-Informed Planning

We introduce Geometry-Informed Planning (GIP), a novel planning framework for offline goal-conditioned reinforcement learning (GCRL). GIP views the state space as a smooth manifold, where temporal distance is defined by optimal goal-reaching time. Optimal trajectories then correspond to geodesics, which can be represented by initial tangent vectors through the exponential map. Guided by this geometric structure, GIP represents an entire path with a single latent path vector and learns to sample such vectors for arbitrary state-goal pairs to infer geodesics. Our geometric formulation enables theoretical recovery of optimal goal-reaching paths under suitable assumptions, while joint learning of temporal distances with generated paths discourages invalid shortcuts that leave the state manifold. GIP enables efficient planning with a fixed-dimensional latent vector independent of the planning horizon, while training without temporal difference learning supports its scalability. We empirically validate these properties on OGBench, where GIP outperforms model-free and model-based baselines, particularly on long-horizon tasks, while requiring substantially lower planning cost.