Title: The Cost of Multi-Group Transductive Learning

Abstract:

This study demonstrates that in the transductive framework, any multi-group learner faces a multiplicative increase in its error rate for certain groups compared to what is possible in a single-group context. This penalty can scale linearly with the number of groups, reaching approximately the square root of the sample size. This finding presents a significant divergence from optimal multi-group learners in a comparable group-realizable statistical environment, where the error penalty remains bounded by a logarithmic factor of the sample size and does not depend on the quantity of groups.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC