Keywords: Transfer learning ∙ Domain adaptation ∙ Learning theory

1. Introduction

2. Transductive transfer learning where \( \mathcal{S}_{\mathbf{X}}\neq\mathcal{T}_{\mathbf{X}} \) but \( t_{S}=t_{T} \)

2. Preliminary knowledge

2.1 Definitions

2.2 Probably approximately correct setting

2.3 Vapnik-Chervonenkis complexity

2.4 Rademacher complexity

2.5 PAC-Bayesian bounds

2.6 Uniform stability

2.7 Algorithmic robustness

3. Seminal divergence-based learning bounds

4. Hardness results for domain adaptation

5. Learning bounds with integral probability metrics

6. PAC-Bayesian theory for domain adaptation

7. Domain adaptation theory based on algorithmic properties

8. Conclusions and discussion