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Test score algorithms for budgeted stochastic utility maximization

Lee, Dabeen, Vojnovic, Milan and Yun, Se-young (2022) Test score algorithms for budgeted stochastic utility maximization. INFORMS Journal on Optimization. ISSN 2575-1484

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Identification Number: 10.1287/ijoo.2022.0075

Abstract

Motivated by recent developments in designing algorithms based on individual item scores for solving utility maximization problems, we study the framework of using test scores, defined as a statistic of observed individual item performance data, for solving the budgeted stochastic utility maximization problem. We extend an existing scoring mechanism, namely, the replication test scores, to incorporate heterogeneous item costs as well as item values. We show that a natural greedy algorithm that selects items solely based on their replication test scores outputs solutions within a constant factor of the optimum for the class of functions satisfying an extended diminishing returns property. Our algorithms and approximation guarantees assume that test scores are noisy estimates of certain expected values with respect to marginal distributions of individual item values, thus making our algorithms practical and extending previous work that assumes noiseless estimates. Moreover, we show how our algorithm can be adapted to the setting in which items arrive in a streaming fashion while maintaining the same approximation guarantee. We present numerical results, using synthetic data and data sets from the Academia.StackExchange Q&A forum, which show that our test score algorithm can achieve competitiveness and in some cases better performance than a benchmark algorithm that requires access to a value oracle to evaluate function values.

Item Type: Article
Official URL: https://pubsonline.informs.org/journal/ijoo
Additional Information: © 2022 INFORMS
Divisions: Statistics
Date Deposited: 30 Sep 2022 10:18
Last Modified: 31 Oct 2022 15:51
URI: http://eprints.lse.ac.uk/id/eprint/116716

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