Parallel Algorithm for Non-Monotone DR-Submodular Maximization

Alina Ene, Huy Nguyen
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:2902-2911, 2020.

Abstract

In this work, we give a new parallel algorithm for the problem of maximizing a non-monotone diminishing returns submodular function subject to a cardinality constraint. For any desired accuracy $\epsilon$, our algorithm achieves a $1/e - \epsilon$ approximation using $O(\log{n} \log(1/\epsilon) / \epsilon^3)$ parallel rounds of function evaluations. The approximation guarantee nearly matches the best approximation guarantee known for the problem in the sequential setting and the number of parallel rounds is nearly-optimal for any constant $\epsilon$. Previous algorithms achieve worse approximation guarantees using $\Omega(\log^2{n})$ parallel rounds. Our experimental evaluation suggests that our algorithm obtains solutions whose objective value nearly matches the value obtained by the state of the art sequential algorithms, and it outperforms previous parallel algorithms in number of parallel rounds, iterations, and solution quality.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-ene20a, title = {Parallel Algorithm for Non-Monotone {DR}-Submodular Maximization}, author = {Ene, Alina and Nguyen, Huy}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {2902--2911}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/ene20a/ene20a.pdf}, url = {https://proceedings.mlr.press/v119/ene20a.html}, abstract = {In this work, we give a new parallel algorithm for the problem of maximizing a non-monotone diminishing returns submodular function subject to a cardinality constraint. For any desired accuracy $\epsilon$, our algorithm achieves a $1/e - \epsilon$ approximation using $O(\log{n} \log(1/\epsilon) / \epsilon^3)$ parallel rounds of function evaluations. The approximation guarantee nearly matches the best approximation guarantee known for the problem in the sequential setting and the number of parallel rounds is nearly-optimal for any constant $\epsilon$. Previous algorithms achieve worse approximation guarantees using $\Omega(\log^2{n})$ parallel rounds. Our experimental evaluation suggests that our algorithm obtains solutions whose objective value nearly matches the value obtained by the state of the art sequential algorithms, and it outperforms previous parallel algorithms in number of parallel rounds, iterations, and solution quality.} }
Endnote
%0 Conference Paper %T Parallel Algorithm for Non-Monotone DR-Submodular Maximization %A Alina Ene %A Huy Nguyen %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-ene20a %I PMLR %P 2902--2911 %U https://proceedings.mlr.press/v119/ene20a.html %V 119 %X In this work, we give a new parallel algorithm for the problem of maximizing a non-monotone diminishing returns submodular function subject to a cardinality constraint. For any desired accuracy $\epsilon$, our algorithm achieves a $1/e - \epsilon$ approximation using $O(\log{n} \log(1/\epsilon) / \epsilon^3)$ parallel rounds of function evaluations. The approximation guarantee nearly matches the best approximation guarantee known for the problem in the sequential setting and the number of parallel rounds is nearly-optimal for any constant $\epsilon$. Previous algorithms achieve worse approximation guarantees using $\Omega(\log^2{n})$ parallel rounds. Our experimental evaluation suggests that our algorithm obtains solutions whose objective value nearly matches the value obtained by the state of the art sequential algorithms, and it outperforms previous parallel algorithms in number of parallel rounds, iterations, and solution quality.
APA
Ene, A. & Nguyen, H.. (2020). Parallel Algorithm for Non-Monotone DR-Submodular Maximization. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:2902-2911 Available from https://proceedings.mlr.press/v119/ene20a.html.

Related Material