Test Score Algorithms for Budgeted Stochastic Utility Maximization

TL;DR

This paper develops and analyzes test score-based algorithms for budgeted stochastic utility maximization, extending existing methods to heterogeneous costs and noisy data, with proven approximation guarantees and practical streaming adaptations.

Contribution

It extends replication test scores to heterogeneous and noisy settings, providing a greedy algorithm with constant-factor approximation guarantees for utility maximization.

Findings

The greedy test score algorithm achieves solutions within a constant factor of the optimum.

The approach is effective with noisy estimates of item performance.

Numerical results show competitive or superior performance to oracle-based benchmarks.

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 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.