Shortest Path under Uncertainty: Exploration versus Exploitation

In the Canadian Traveler Problem (CTP), a traveler seeks a shortest path to a destination through a road network, but unknown to the traveler, some roads may be blocked. This paper studies the Bayesian CTP (BCTP), in which road states are correlated with known prior probabilities and the traveler can infer the states of an unseen road from past observations of other correlated roads. As generalized shortest-path problems, CTP and BCTP have important practical applications. We show that BCTP is NP-complete and give a polynomial-time approximation algorithm, Hedged Shortest Path under Determinization (HSPD), which approximates an optimal solution with a polylogarithmic factor. Preliminary experiments show promising results. HSPD outperforms a widely used greedy algorithm and a state-of-the-art UCT-based search algorithm for CTP, especially when significant exploration is required.