Dijkstra as an Oracle for Online Stochastic Shortest Path Navigation with Provable Guarantees

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Classical robot path planning under uncertainty usually forces a choice: value iteration is exact but scales poorly with map size, while Dijkstra is fast but considered approximate once transitions become stochastic. This paper challenges that tradeoff. The authors prove that Dijkstra's algorithm can be an exact oracle under a condition weaker than the standard causality assumption: nonnegativity of a reduced cost on the determinized map. Building on this theoretical result, they propose DORA (Dijkstra Oracle Reduced-cost Algorithm), an online learner that calls a shortest-path oracle a fixed number of times per episode without ever estimating a transition kernel. In grid-world navigation, directional drilling, and drone surveillance benchmarks, DORA matches the performance of optimistic value iteration given the true transition kernel while doing 4.5 to 19.3 times less planner work. It also reduces obstacle contacts during learning by a factor of 17 compared to determinize-and-replan baselines, and satisfies contact-rate budgets spanning two orders of magnitude via a logarithmic survival weight. The practical implication is that classical graph-search infrastructure can underpin safe, efficient online robot navigation without the memory and compute overhead of explicit stochastic planning.