Robustification of Online Graph Exploration Methods

Abstract

Exploring unknown environments is a fundamental task in many domains, e.g., robot navigation, network security, and internet search. We initiate the study of a learning-augmented variant of the classical, notoriously hard online graph exploration problem by adding access to machine-learned predictions. We propose an algorithm that naturally integrates predictions into the well-known Nearest Neighbor (NN) algorithm and significantly outperforms any known online algorithm if the prediction is of high accuracy while maintaining good guarantees when the prediction is of poor quality. We provide theoretical worst-case bounds that gracefully degrade with the prediction error, and we complement them by computational experiments that confirm our results. Further, we extend our concept to a general framework to robustify algorithms. By interpolating carefully between a given algorithm and NN, we prove new performance bounds that leverage the individual good performance on particular inputs while establishing robustness to arbitrary inputs.

Contract Scheduling with Predictions

“…There are several recent works that study algorithms with machine-learned predictions in a status of uncertainty. Examples include online rent-or-buy problems with multiple expert predictions (Gollapudi & Panigrahi, 2019), queuing systems with job service times predicted by an oracle (Mitzenmacher, 2020), online algorithms for metrical task systems (Antoniadis, Coester, Elias, Polak, & Simon, 2020), online makespan scheduling (Lattanzi, Lavastida, Moseley, & Vassilvitskii, 2020), graph exploration (Eberle, Lindermayr, Megow, Nölke, & Schlöter, 2022) and the Steiner tree problem (Xu & Moseley, 2022), to mention only some representative results. See also the survey (Mitzenmacher & Vassilvitskii, 2020).…”

Paging with Succinct Predictions

“…Other learning-augmented online algorithms. In addition to the already mentioned results on learning-augmented paging, several exciting learning-augmented algorithms have been developed for various online problems, including among others weighted paging [7], k-server [28], metrical task systems [2], ski-rental [36,3], non-clairvoyant scheduling [36,27], online-knapsack [23,43,12], secretary and matching problems [16,5], graph exploration [17], as well as energy-efficient scheduling [6,4,3]. Machine-learned predictions have also been considered for designing offline algorithms with an improved running time, see for instance the results of Dinitz et al [14] on matchings, Chen et al [13] on graph algorithms, Ergun et al [19] on k-means clustering, Sakaue and Oki [38] on discrete optimization, and Polak and Zub [35] on maximum flows.…”

Competitive search in a network

“…Subsequent work (Angelopoulos, 2023) improved some of these bounds, and extended other to the m-ray search problems, assuming again pure strategies. (Eberle et al, 2022) showed how to robustify graph exploration algorithms that leverage a prediction on the minimum spanning tree of the explored graph. (Banerjee et al, 2023) studied graph search algorithms in a setting in which vertex of the graph can provide an imperfect estimation of the distance of the said vertex to the target.…”

“…[9] studied a graph search setting where every node in the graph provides a prediction of its distance to the target vertex. [22] showed how to robustify graph exploration algorithms, where the prediction is related to the spanning tree of the explored graph.…”