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Motivated by recent developments in designing algorithms based on individualitem scores for solving utility maximization problems, we study the frameworkof using test scores, defined as a statistic of observed individual itemperformance data, for solving the budgeted stochastic utility maximizationproblem. We extend an existing scoring mechanism, namely the replication testscores, to incorporate heterogeneous item costs as well as item values. We showthat a natural greedy algorithm that selects items solely based on theirreplication test scores outputs solutions within a constant factor of theoptimum for a broad class of utility functions. Our algorithms andapproximation guarantees assume that test scores are noisy estimates of certainexpected values with respect to marginal distributions of individual itemvalues, thus making our algorithms practical and extending previous work thatassumes noiseless estimates. Moreover, we show how our algorithm can be adaptedto the setting where items arrive in a streaming fashion while maintaining thesame approximation guarantee. We present numerical results, using syntheticdata and data sets from the Academia.StackExchange Q&A forum, which show thatour test score algorithm can achieve competitiveness, and in some cases betterperformance than a benchmark algorithm that requires access to a value oracleto evaluate function values.

Test Score Algorithms for Budgeted Stochastic Utility Maximization