The Power and Limitation of Pretraining-Finetuning for Linear Regression under Covariate Shift

• URL: http://arxiv.org/abs/2208.01857v1
• Date: Wed, 3 Aug 2022 05:59:49 GMT
• Title: The Power and Limitation of Pretraining-Finetuning for Linear Regression under Covariate Shift
• Authors: Jingfeng Wu and Difan Zou and Vladimir Braverman and Quanquan Gu and Sham M. Kakade
• Abstract summary: We investigate a transfer learning approach with pretraining on the source data and finetuning based on the target data. For a large class of linear regression instances, transfer learning with $O(N2)$ source data is as effective as supervised learning with $N$ target data.
• Score: 127.21287240963859
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study linear regression under covariate shift, where the marginal distribution over the input covariates differs in the source and the target domains, while the conditional distribution of the output given the input covariates is similar across the two domains. We investigate a transfer learning approach with pretraining on the source data and finetuning based on the target data (both conducted by online SGD) for this problem. We establish sharp instance-dependent excess risk upper and lower bounds for this approach. Our bounds suggest that for a large class of linear regression instances, transfer learning with $O(N^2)$ source data (and scarce or no target data) is as effective as supervised learning with $N$ target data. In addition, we show that finetuning, even with only a small amount of target data, could drastically reduce the amount of source data required by pretraining. Our theory sheds light on the effectiveness and limitation of pretraining as well as the benefits of finetuning for tackling covariate shift problems.

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