Cost-to-Go Estimation by Decomposed Latent Path Integration

Estimating the effort required to reach a goal from a given state is a fundamental problem in planning and control. Many recent approaches estimate this cost by encoding the start and goal observations independently and computing a metric or quasimetric between their representations. This paper introduces decomposed latent path integration (DeLPI), an architectural primitive that estimates distance through accumulated motion in latent space. In our instantiation, the two observations are jointly encoded into a spatial grid of latent vectors, which is iteratively updated by a depth-recurrent module. The predicted distance is computed as the sum of the latent vector displacements produced over these updates. We compare our method against metric, quasimetric, and joint-encoding baselines on four environments with nontrivial combinatorial structure: Switchyard, a gridworld with a controllable degree of factor coupling; Sokoban; Rubik's cube; and Craftax. Across these environments, it either outperforms the baselines or achieves comparable performance with substantially fewer parameters. More broadly, our experiments show that, in these environments, architectures that jointly process the start and goal states consistently outperform approaches that embed the two states independently.