Stability-Aware Bilevel Source Dataset Selection for Importance-Weighted Least Squares in Unsupervised Domain Adaptation

Importance-weighted least squares (IWLS) is widely used to correct covariate shift in unsupervised domain adaptation, yet most prior work assumes that an appropriate source dataset is already available. In practical internet-scale retrieval settings, the key decision is reversed: given only unlabeled target covariates and a pool of candidate source datasets, which source (or source mixture) should be selected before fitting a weighted regressor? We study this question through a stability-aware bilevel framework with three formal components: a label-free source-ranking surrogate with a uniform regret guarantee, a multi-source mixture objective with linear-rate upper-level optimization under smoothness and strong-convexity assumptions, and a mixed-shift gate for harmful-source rejection before weighted fitting. We evaluate these components in three settings (distribution-level synthetic shift, semi-synthetic target-sample selection, and a protocol-faithful proxy real-track setting with governance checks). The empirical findings are mixed: symbolic checks and theorem-conditioned diagnostics are consistent, but Holm-corrected comparisons show no statistically significant advantage of the stability-aware selector over MMD-nearest, Wasserstein-nearest, or pooled IWLS in the current iter\_1 run. This outcome clarifies that optimization guarantees and diagnostic structure are not sufficient for global predictive dominance under the present proxy data regime. The study contributes a reproducible no-target-label protocol, explicit failure reporting, and a concrete follow-up agenda for real benchmark ingestion and post-selection-controlled confirmatory analysis.