Learning-Based Algorithms for Graph Searching Problems

TL;DR

This paper develops algorithms for graph searching with noisy distance predictions, providing formal guarantees on unknown weighted graphs, demonstrating robustness to errors, and improving understanding of known graph search bounds.

Contribution

It introduces algorithms with optimal guarantees for graph search with noisy predictions on unknown graphs and analyzes their performance and bounds.

Findings

Algorithms are robust to adversarial and stochastic errors.

First formal guarantees for unknown weighted graphs.

New bounds for search on known graphs.

Abstract

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.