Learning Augmented Online Facility Location

Following the research agenda initiated by Munoz & Vassilvitskii [1] and Lykouris & Vassilvitskii [2] on learning-augmented online algorithms for classical online optimization problems, in this work, we consider the Online Facility Location problem under this framework. In Online Facility Location (OFL), demands arrive one-by-one in a metric space and must be (irrevocably) assigned to an open facility upon arrival, without any knowledge about future demands. We present an online algorithm for OFL that exploits potentially imperfect predictions on the locations of the optimal facilities. We prove that the competitive ratio decreases smoothly from sublogarithmic in the number of demands to constant, as the error, i.e., the total distance of the predicted locations to the optimal facility locations, decreases towards zero. We complement our analysis with a matching lower bound establishing that the dependence of the algorithm’s competitive ratio on the error is optimal, up to constant factors. Finally, we evaluate our algorithm on real world data and compare our learning augmented approach with the current best online algorithm for the problem.

[1]  Adam Meyerson,et al.  Online facility location , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[2]  Amos Fiat,et al.  Competitive Paging Algorithms , 1991, J. Algorithms.

[3]  Dimitris Fotakis,et al.  Online and incremental algorithms for facility location , 2011, SIGA.

[4]  Zvi Drezner,et al.  Facility location - applications and theory , 2001 .

[5]  Piotr Sankowski,et al.  Online Facility Location with Deletions , 2018, ESA.

[6]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[7]  Michael Mitzenmacher,et al.  Scheduling with Predictions and the Price of Misprediction , 2019, ITCS.

[8]  Alexander Wei,et al.  Better and Simpler Learning-Augmented Online Caching , 2020, APPROX-RANDOM.

[9]  Antonios Antoniadis,et al.  Secretary and Online Matching Problems with Machine Learned Advice , 2020, NeurIPS.

[10]  Janardhan Kulkarni,et al.  On the Facility Location Problem in Online and Dynamic Models , 2020, APPROX-RANDOM.

[11]  Sergei Vassilvitskii,et al.  Revenue Optimization with Approximate Bid Predictions , 2017, NIPS.

[12]  Andrew Chi-Chih Yao,et al.  Probabilistic computations: Toward a unified measure of complexity , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[13]  Said Salhi,et al.  Discrete Location Theory , 1991 .

[14]  Silvio Lattanzi,et al.  Online Scheduling via Learned Weights , 2020, SODA.

[15]  Ola Svensson,et al.  Learning Augmented Energy Minimization via Speed Scaling , 2020, NeurIPS.

[16]  David B. Shmoys,et al.  Approximation algorithms for facility location problems , 2000, APPROX.

[17]  Russell Bent,et al.  A simple and deterministic competitive algorithm for online facility location , 2004, Inf. Comput..

[18]  Google,et al.  Improving Online Algorithms via ML Predictions , 2024, NeurIPS.

[19]  Nikos Parotsidis,et al.  Fully Dynamic Consistent Facility Location , 2019, NeurIPS.

[20]  Dimitris Fotakis.  A Primal-Dual Algorithm for Online Non-uniform Facility Location , 2005, Panhellenic Conference on Informatics.

[21]  Dimitris Fotakis,et al.  On the Competitive Ratio for Online Facility Location , 2003, Algorithmica.

[22]  Dhruv Rohatgi,et al.  Near-Optimal Bounds for Online Caching with Machine Learned Advice , 2019, SODA.

[23]  Sreenivas Gollapudi,et al.  Online Algorithms for Rent-Or-Buy with Expert Advice , 2019, ICML.

[24]  Ola Svensson,et al.  The Primal-Dual method for Learning Augmented Algorithms , 2020, NeurIPS.

[25]  A. Hoorfar,et al.  INEQUALITIES ON THE LAMBERTW FUNCTION AND HYPERPOWER FUNCTION , 2008 .

[26]  Sergei Vassilvitskii,et al.  Competitive caching with machine learned advice , 2018, ICML.

[27]  Amin Saberi,et al.  Online Optimization with Uncertain Information , 2012, ACM Trans. Algorithms.