Dijkstra's Algorithm Shown Exact for Stochastic Navigation with DORA Online Learning
A study posted on arXiv re-examines the use of Dijkstra's algorithm for stochastic shortest path planning in mobile robot navigation. Robots working alongside humans in critical infrastructure must minimize travel costs despite uncertain map traversal times and imperfect actuation. Exact methods such as value iteration are computationally heavy, scaling with the map's diameter, while Dijkstra is fast yet generally considered inaccurate when transitions are stochastic. The paper proves that Dijkstra's algorithm can serve as an exact planner under a condition far less restrictive than the usual causality assumption: the reduced cost defined on the determinized map must be nonnegative. Based on this characterization, the authors introduce DORA (Dijkstra Oracle Reduced-cost Algorithm), an online learner that invokes a shortest-path oracle a fixed number of times per episode and avoids estimating transition models. The paper is available at arXiv:2608.17703.
Key facts
- Paper announced on arXiv as arXiv:2608.17703v1.
- Study focuses on mobile robots operating near humans and in critical facilities.
- Robots face unknown true traversal costs and imperfect actuation.
- Value iteration provides exact solutions but requires computation proportional to map diameter.
- Dijkstra's algorithm is fast but traditionally considered inexact for stochastic transitions.
- The research identifies a condition—nonnegative reduced cost on the determinized map—under which Dijkstra's algorithm is exact.
- This condition is weaker than the causality condition often required in the literature.
- The proposed DORA algorithm calls a shortest-path oracle a fixed number of times per episode and never estimates a transition model.
Entities
Artists
- Edsger Dijkstra
Institutions
- arXiv