Learning-Based Algorithms for Graph Searching Problems

Adela F. DePavia, Erasmo Tani, Ali Vakilian
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:928-936, 2024.

Abstract

We consider the problem of graph searching with prediction recently introduced by Banerjee et al. (2023). 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 traveled. 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 simpler performance bounds on the algorithms of Banerjee et al. (2023) for the case of searching on a known graph and establish new lower bounds for this setting.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-depavia24a, title = { Learning-Based Algorithms for Graph Searching Problems }, author = {DePavia, Adela F. and Tani, Erasmo and Vakilian, Ali}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {928--936}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/depavia24a/depavia24a.pdf}, url = {https://proceedings.mlr.press/v238/depavia24a.html}, abstract = { We consider the problem of graph searching with prediction recently introduced by Banerjee et al. (2023). 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 traveled. 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 simpler performance bounds on the algorithms of Banerjee et al. (2023) for the case of searching on a known graph and establish new lower bounds for this setting. } }
Endnote
%0 Conference Paper %T Learning-Based Algorithms for Graph Searching Problems %A Adela F. DePavia %A Erasmo Tani %A Ali Vakilian %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-depavia24a %I PMLR %P 928--936 %U https://proceedings.mlr.press/v238/depavia24a.html %V 238 %X We consider the problem of graph searching with prediction recently introduced by Banerjee et al. (2023). 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 traveled. 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 simpler performance bounds on the algorithms of Banerjee et al. (2023) for the case of searching on a known graph and establish new lower bounds for this setting.
APA
DePavia, A.F., Tani, E. & Vakilian, A.. (2024). Learning-Based Algorithms for Graph Searching Problems . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:928-936 Available from https://proceedings.mlr.press/v238/depavia24a.html.

Related Material