Learning Combinatorial Functions from Pairwise Comparisons
This addresses the challenge of learning real-valued combinatorial functions in domains like microeconomics and social networks where obtaining cardinal labels is difficult, offering a practical alternative for applications with pairwise preference data.
The paper tackles the problem of learning combinatorial functions when only pairwise comparisons are available, presenting novel algorithms that achieve learning guarantees for a wide range of function classes, including coverage, submodular, XOS, and subadditive functions.
A large body of work in machine learning has focused on the problem of learning a close approximation to an underlying combinatorial function, given a small set of labeled examples. However, for real-valued functions, cardinal labels might not be accessible, or it may be difficult for an expert to consistently assign real-valued labels over the entire set of examples. For instance, it is notoriously hard for consumers to reliably assign values to bundles of merchandise. Instead, it might be much easier for a consumer to report which of two bundles she likes better. With this motivation in mind, we consider an alternative learning model, wherein the algorithm must learn the underlying function up to pairwise comparisons, from pairwise comparisons. In this model, we present a series of novel algorithms that learn over a wide variety of combinatorial function classes. These range from graph functions to broad classes of valuation functions that are fundamentally important in microeconomic theory, the analysis of social networks, and machine learning, such as coverage, submodular, XOS, and subadditive functions, as well as functions with sparse Fourier support.