Using Partial Monotonicity in Submodular Maximization

Mualem, Loay; Feldman, Moran

doi:10.48550/arxiv.2202.03051

Cited by 4 publications

(7 citation statements)

References 25 publications

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“…To tackle this problem, we reformulate it into a cardinality-constrained set function optimization task. Subsequently, we introduce novel set function properties, (m, m)-partial monotonicity and (γ, γ)-weak submodularity, extending recent notions of partial monotonicity (Mualem and Feldman 2022) and approximate submodularity (Elenberg et al 2018;Harshaw et al 2019;De et al 2021). These properties allow us to design a greedy algorithm GENEX, to compute near-optimal feature subsets, with new approximation guarantee.…”

Section: Discrete Continuous Training Frameworkmentioning

confidence: 99%

Generator Assisted Mixture of Experts for Feature Acquisition in Batch

Asgaonkar,

Jain,

2024

AAAI

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Given a set of observations, feature acquisition is about finding the subset of unobserved features which would enhance accuracy. Such problems has been explored in a sequential setting in prior work. Here, the model receives feedback from every new feature acquireed and chooses to explore more features or to predict. However, sequential acquisition is not feasible in some settings where time is of essence. We consider the problem of feature acquisition in batch, where the subset of features to be queried in batch is chosen based on the currently observed features, and then acquired as a batch, followed by prediction. We solve this problem using several technical innovations. First, we use a feature generator to draw a subset of the synthetic features for some examples, which reduces the cost of oracle queries. Second, to make the feature acquisition problem tractable for the large heterogeneous observed features, we partition the data into buckets, by borrowing tools from locality sensitive hashing and then train a mixture of experts model. Third, we design a tractable lower bound of the original objective. We use a greedy algorithm combined with model training to solve the underlying problem. Experiments with four datasets shows that our approach outperforms these methods in terms of trade off between accuracy and feature acquisition cost.

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Section: Discrete Continuous Training Frameworkmentioning

confidence: 99%

Generator Assisted Mixture of Experts for Feature Acquisition in Batch

Asgaonkar,

Jain,

2024

AAAI

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“…Definition 1 [2] Given any non-negative set function G: 2 N ! R C , the monotonicity ratio of this function is defined as the scalar m G 2 OE0; 1, such that,…”

Section: Preliminarymentioning

confidence: 99%

“…That means that there exist gaps in approximation ratios between the monotonic and non-monotonic submodular optimization problems. For non-negative set functions [2] , there is also a parameter of monotonicity ratio that measures how much of the function is monotonic.…”

Section: Introductionmentioning

confidence: 99%

Approximating ($m_{B},m_{P}$)-Monotone BP Maximization and Extensions

Yang

Gao

Han

et al. 2023

Tsinghua Sci. Technol.

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The paper proposes the optimization problem of maximizing the sum of suBmodular and suPermodular (BP) functions with partial monotonicity under a streaming fashion. In this model, elements are randomly released from the stream and the utility is encoded by the sum of partial monotone suBmodular and suPermodular functions.The goal is to determine whether a subset from the stream of size bounded by parameter k subject to the summarized utility is as large as possible. In this work, a threshold-based streaming algorithm is presented for the BP maximization that attains a ..1 Ä/=.2 Ä/ O."//-approximation with O.1=" 4 log 3 .1="/ log..2 Ä/k=.1 Ä/ 2 // memory complexity, where Ä denotes the parameter of supermodularity ratio. We further consider a more general model with fair constraints and present a greedy-based algorithm that obtains the same approximation. We finally investigate this fair model under the streaming fashion and provide a ..1 Ä/ 4 =.2 2Ä C Ä 2 / 2 O."//-approximation algorithm.

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“…Recently, Iyer (2015) introduced the concept of monotonicity ratio, a continuous version of monotonicity, under the non-adaptive setting. Mualem and Feldman (2022) provides a systematical study about this property.…”

Section: Additional Related Workmentioning

confidence: 99%

Partial-Monotone Adaptive Submodular Maximization

Tang¹,

Yuan²

2022

Preprint

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Many sequential decision making problems, including pool-based active learning and adaptive viral marketing, can be formulated as an adaptive submodular maximization problem. The input of this problem is a group of items and each item has a random state whose realization is unknown initially, one must pick an item before observing its realization. The objective is to adaptively select a group of items to maximize an adaptive submodular utility function, which is defined over items and states. Most of existing studies on adaptive submodular optimization focus on either monotone case or non-monotone case. Specifically, if the utility function is monotone and adaptive submodular, Golovin and Krause (2011) developed a greedy policy that achieves a (1 − 1/e) approximation ratio subject to a cardinality constraint. If the utility function is non-monotone and adaptive submodular, Tang (2021a) showed that a random greedy policy achieves a 1/e approximation ratio subject to a cardinality constraint. In this work, we aim to generalize the above mentioned results by studying the partial-monotone adaptive submodular maximization problem. To this end, we introduce the notation of adaptive monotonicity ratio m ∈ [0, 1] to measure the degree of monotonicity of a function. Our main result is to show that a random greedy policy achieves an approximation ratio of m(1 − 1/e) + (1 − m)(1/e) if the utility function is m-adaptive monotone and adaptive submodular. Notably this result recovers the aforementioned (1 − 1/e) and 1/e approximation ratios when m = 0 and m = 1, respectively. We further extend our results to consider a knapsack constraint. We show that a sampling-based policy achieves an approximation ratio of (m + 1)/10 if the utility function is m-adaptive monotone and adaptive submodular. One important implication of our results is that even for a non-monotone utility function, we still can achieve an approximation ratio close to (1 − 1/e) if this function is "close" to a monotone function. This leads to improved performance bounds for many machine learning applications whose utility functions are almost adaptive monotone.

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Using Partial Monotonicity in Submodular Maximization

Cited by 4 publications

References 25 publications

Generator Assisted Mixture of Experts for Feature Acquisition in Batch

Generator Assisted Mixture of Experts for Feature Acquisition in Batch

Approximating ($m_{B},m_{P}$)-Monotone BP Maximization and Extensions

Partial-Monotone Adaptive Submodular Maximization

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