License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2021.69
URN: urn:nbn:de:0030-drops-155029
Go to the corresponding LIPIcs Volume Portal

Tang, Shaojie ; Yuan, Jing

Adaptive Regularized Submodular Maximization

LIPIcs-ISAAC-2021-69.pdf (0.7 MB)


In this paper, we study the problem of maximizing the difference between an adaptive submodular (revenue) function and a non-negative modular (cost) function. The input of our problem is a set of n items, where each item has a particular state drawn from some known prior distribution The revenue function g is defined over items and states, and the cost function c is defined over items, i.e., each item has a fixed cost. The state of each item is unknown initially and one must select an item in order to observe its realized state. A policy π specifies which item to pick next based on the observations made so far. Denote by g_{avg}(π) the expected revenue of π and let c_{avg}(π) denote the expected cost of π. Our objective is to identify the best policy π^o ∈ arg max_π g_{avg}(π)-c_{avg}(π) under a k-cardinality constraint. Since our objective function can take on both negative and positive values, the existing results of submodular maximization may not be applicable. To overcome this challenge, we develop a series of effective solutions with performance guarantees. Let π^o denote the optimal policy. For the case when g is adaptive monotone and adaptive submodular, we develop an effective policy π^l such that g_{avg}(π^l) - c_{avg}(π^l) ≥ (1-1/e-ε)g_{avg}(π^o) - c_{avg}(π^o), using only O(nε^{-2}log ε^{-1}) value oracle queries. For the case when g is adaptive submodular, we present a randomized policy π^r such that g_{avg}(π^r) - c_{avg}(π^r) ≥ 1/eg_{avg}(π^o) - c_{avg}(π^o).

BibTeX - Entry

  author =	{Tang, Shaojie and Yuan, Jing},
  title =	{{Adaptive Regularized Submodular Maximization}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{69:1--69:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-155029},
  doi =		{10.4230/LIPIcs.ISAAC.2021.69},
  annote =	{Keywords: Adaptive submodularity, approximation algorithms, active learning}

Keywords: Adaptive submodularity, approximation algorithms, active learning
Collection: 32nd International Symposium on Algorithms and Computation (ISAAC 2021)
Issue Date: 2021
Date of publication: 30.11.2021

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI