  We consider the problem of graph searching with prediction recently
introduced by Banerjee et al. (2022). In this problem, an agent, starting at
some vertex $r$ has to traverse a (potentially unknown) graph $G$ to find a
hidden goal node $g$ while minimizing the total distance travelled. We study a
setting in which at any node $v$, the agent receives a noisy estimate of the
distance from $v$ to $g$. We design algorithms for this search task on unknown
graphs. We establish the first formal guarantees on unknown weighted graphs and
provide lower bounds showing that the algorithms we propose have optimal or
nearly-optimal dependence on the prediction error. Further, we perform
numerical experiments demonstrating that in addition to being robust to
adversarial error, our algorithms perform well in typical instances in which
the error is stochastic. Finally, we provide alternative simpler performance
bounds on the algorithms of Banerjee et al. (2022) for the case of searching on
a known graph, and establish new lower bounds for this setting.
