## Adaptive Submodularity: A New Approach to Active Learning and Stochastic Optimization

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Citations: | 17 - 2 self |

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@MISC{Golovin_adaptivesubmodularity:,

author = {Daniel Golovin and Andreas Krause},

title = {Adaptive Submodularity: A New Approach to Active Learning and Stochastic Optimization},

year = {}

}

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### Abstract

Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions to adaptive policies. We prove that if a problem satisfies this property, a simple adaptive greedy algorithm is guaranteed to be competitive with the optimal policy. We illustrate the usefulness of the concept by giving several examples of adaptive submodular objectives arising in diverse applications including sensor placement, viral marketing and pool-based active learning. Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases and leads to natural generalizations. 1

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Citation Context ...ing on Ψ ′ by taking the expectation over all Ψ ′ consistent with Ψ, we infer S stochastically dominates S ′ , which completes the proof. 7 Application: Active Learning In pool-based active learning (=-=McCallum & Nigam, 1998-=-), we are given a set of hypotheses H, and a set of unlabeled data points X where each x ∈ X is independently drawn from some distribution D. Let L be the set of possible labels. The goal is to adapti... |

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Citation Context ...the case of binary labels L = {−1, 1}, various authors have considered greedy policies which generalize binary search (Garey & Graham, 1974; Loveland, 1985; Arkin et al., 1993; Kosaraju et al., 1999; =-=Dasgupta, 2004-=-; Guillory & Bilmes, 2009; Nowak, 2009). The simplest of these, called generalized binary search (GBS) or the splitting algorithm, works as follows. Define the version space V to be the set of hypothe... |

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Citation Context ...hesis h and thus error(h) depend on it. In the case of binary labels L = {−1, 1}, various authors have considered greedy policies which generalize binary search (Garey & Graham, 1974; Loveland, 1985; =-=Arkin et al., 1993-=-; Kosaraju et al., 1999; Dasgupta, 2004; Guillory & Bilmes, 2009; Nowak, 2009). The simplest of these, called generalized binary search (GBS) or the splitting algorithm, works as follows. Define the v... |

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Citation Context ...rious authors have considered greedy policies which generalize binary search (Garey & Graham, 1974; Loveland, 1985; Arkin et al., 1993; Kosaraju et al., 1999; Dasgupta, 2004; Guillory & Bilmes, 2009; =-=Nowak, 2009-=-). The simplest of these, called generalized binary search (GBS) or the splitting algorithm, works as follows. Define the version space V to be the set of hypotheses consistent with the observed label... |

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Citation Context ...ith respect to D(X); the learned hypothesis h and thus error(h) depend on it. In the case of binary labels L = {−1, 1}, various authors have considered greedy policies which generalize binary search (=-=Garey & Graham, 1974-=-; Loveland, 1985; Arkin et al., 1993; Kosaraju et al., 1999; Dasgupta, 2004; Guillory & Bilmes, 2009; Nowak, 2009). The simplest of these, called generalized binary search (GBS) or the splitting algor... |

22 |
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(Show Context)
Citation Context ...or(h) depend on it. In the case of binary labels L = {−1, 1}, various authors have considered greedy policies which generalize binary search (Garey & Graham, 1974; Loveland, 1985; Arkin et al., 1993; =-=Kosaraju et al., 1999-=-; Dasgupta, 2004; Guillory & Bilmes, 2009; Nowak, 2009). The simplest of these, called generalized binary search (GBS) or the splitting algorithm, works as follows. Define the version space V to be th... |

14 |
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Citation Context ...he learned hypothesis h and thus error(h) depend on it. In the case of binary labels L = {−1, 1}, various authors have considered greedy policies which generalize binary search (Garey & Graham, 1974; =-=Loveland, 1985-=-; Arkin et al., 1993; Kosaraju et al., 1999; Dasgupta, 2004; Guillory & Bilmes, 2009; Nowak, 2009). The simplest of these, called generalized binary search (GBS) or the splitting algorithm, works as f... |

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Citation Context ...ry labels L = {−1, 1}, various authors have considered greedy policies which generalize binary search (Garey & Graham, 1974; Loveland, 1985; Arkin et al., 1993; Kosaraju et al., 1999; Dasgupta, 2004; =-=Guillory & Bilmes, 2009-=-; Nowak, 2009). The simplest of these, called generalized binary search (GBS) or the splitting algorithm, works as follows. Define the version space V to be the set of hypotheses consistent with the o... |

5 | Advances in neural information processing systems - Culotta |

1 | Stochastic submodular maximization. WINE ’08 - Asadpour, Nazerzadeh, et al. - 2008 |