Minimax-optimal Scaling Laws in Ridge Regression via Transfer Learning
Pretrained models are often reused across downstream tasks, motivating the question of whether this transfer learning procedure can provide a substantial performance improvement, namely, in terms of the scaling law. We address this question in the prototypical setting of high-dimensional regression, where (i) a pretrained \emph{source} model is trained via ridge regression, and (ii) a fine-tuned \emph{target} model is regularized via the $L_2$ distance from the source estimator. First, we establish a deterministic equivalent for the risk of this two-step procedure under both model and covariance shift. Next, by specializing the deterministic equivalent to a shared regression function and ...
| Authors | Yalda Shabanzadeh, Diyuan Wu, Marco Mondelli |
|---|---|
| Primary category | cs.LG |
| Published | 16 October 2026 |
| Last updated at source | 16 October 2026 |
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