Filtered Search for Submodular Maximization with Controllable Approximation Bounds
Wenlin Chen, Yixin Chen, Kilian Weinberger
Abstract
Most existing submodular maximization algorithms provide theoretical guarantees with approximation bounds. However, in many cases, users may be interested in an anytime algorithm that can offer a flexible trade-off between computation time and optimality guarantees. In this paper, we propose a filtered search (FS) framework that allows the user to set an arbitrary approximation bound guarantee with a “tunable knob”, from 0 (arbitrarily bad) to 1 (globally optimal). FS naturally handles monotone and non-monotone functions as well as unconstrained problems and problems with cardinality, matroid, and knapsack constraints. Further, it can also be applied to (non-negative) non-submodular functions and still gives controllable approximation bounds based on their submodularity ratio. Finally, FS encompasses the greedy algorithm as a special case. Our framework is based on theory in A* search, but is substantially more efficient because it only requires heuristics that are critically admissible (CA) rather than admissible—a condition that gives more effective pruning and is substantially easier to implement.
BibTeX
@InProceedings{pmlr-v38-chen15c,
title = {{Filtered Search for Submodular Maximization with Controllable Approximation Bounds}},
author = {Chen, Wenlin and Chen, Yixin and Weinberger, Kilian},
booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics},
pages = {156--164},
year = {2015},
editor = {Lebanon, Guy and Vishwanathan, S. V. N.},
volume = {38},
series = {Proceedings of Machine Learning Research},
address = {San Diego, California, USA},
month = {09--12 May},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v38/chen15c.pdf},
url = {https://proceedings.mlr.press/v38/chen15c.html},
abstract = {Most existing submodular maximization algorithms provide theoretical guarantees with approximation bounds. However, in many cases, users may be interested in an anytime algorithm that can offer a flexible trade-off between computation time and optimality guarantees. In this paper, we propose a filtered search (FS) framework that allows the user to set an arbitrary approximation bound guarantee with a “tunable knob”, from 0 (arbitrarily bad) to 1 (globally optimal). FS naturally handles monotone and non-monotone functions as well as unconstrained problems and problems with cardinality, matroid, and knapsack constraints. Further, it can also be applied to (non-negative) non-submodular functions and still gives controllable approximation bounds based on their submodularity ratio. Finally, FS encompasses the greedy algorithm as a special case. Our framework is based on theory in A* search, but is substantially more efficient because it only requires heuristics that are critically admissible (CA) rather than admissible—a condition that gives more effective pruning and is substantially easier to implement.}
}