  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 a broad class of utility functions. 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 where 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.
