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We provide an information-theoretic analy- sis of the generalization ability of Gibbs- based transfer learning algorithms by focus- ing on two popular empirical risk minimiza- tion (ERM) approaches for transfer learning, α-weighted-ERM and two-stage-ERM. Our key result is an exact characterization of the generalization behavior using the conditional symmetrized Kullback-Leibler (KL) informa- tion between the output hypothesis and the target training samples given the source train- ing samples. Our results can also be applied to provide novel distribution-free generaliza- tion error upper bounds on these two afore- mentioned Gibbs algorithms. Our approach is versatile, as it also characterizes the gener- alization errors and excess risks of these two Gibbs algorithms in the asymptotic regime, where they converge to the α-weighted-ERM and two-stage-ERM, respectively. Based on our theoretical results, we show that the ben- efits of transfer learning can be viewed as a bias-variance trade-off, with the bias induced by the source distribution and the variance induced by the lack of target samples. We believe this viewpoint can guide the choice of transfer learning algorithms in practice. 

Various approaches have been developed to upper bound the generalization error of a supervised learning algorithm. However, existing bounds are often loose and lack of guarantees. As a result, they may fail to characterize the exact generalization ability of a learning algorithm.Our main contribution is an exact characterization of the expected generalization error of the well-known Gibbs algorithm (a.k.a. Gibbs posterior) using symmetrized KL information between the input training samples and the output hypothesis. Our result can be applied to tighten existing expected generalization error and PAC-Bayesian bounds. Our approach is versatile, as it also characterizes the generalization error of the Gibbs algorithm with data-dependent regularizer and that of the Gibbs algorithm in the asymptotic regime, where it converges to the empirical risk minimization algorithm. Of particular relevance, our results highlight the role the symmetrized KL information plays in controlling the generalization error of the Gibbs algorithm.