  In transfer learning, training and testing data sets are drawn from different
data distributions. The transfer generalization gap is the difference between
the population loss on the target data distribution and the training loss. The
training data set generally includes data drawn from both source and target
distributions. This work presents novel information-theoretic upper bounds on
the average transfer generalization gap that capture $(i)$ the domain shift
between the target data distribution $P'_Z$ and the source distribution $P_Z$
through a two-parameter family of generalized
$(\alpha_1,\alpha_2)$-Jensen-Shannon (JS) divergences; and $(ii)$ the
sensitivity of the transfer learner output $W$ to each individual sample of the
data set $Z_i$ via the mutual information $I(W;Z_i)$. For $\alpha_1 \in (0,1)$,
the $(\alpha_1,\alpha_2)$-JS divergence can be bounded even when the support of
$P_Z$ is not included in that of $P'_Z$. This contrasts the Kullback-Leibler
(KL) divergence $D_{KL}(P_Z||P'_Z)$-based bounds of Wu et al. [1], which are
vacuous under this assumption. Moreover, the obtained bounds hold for unbounded
loss functions with bounded cumulant generating functions, unlike the
$\phi$-divergence based bound of Wu et al. [1]. We also obtain new upper bounds
on the average transfer excess risk in terms of the $(\alpha_1,\alpha_2)$-JS
divergence for empirical weighted risk minimization (EWRM), which minimizes the
weighted average training losses over source and target data sets. Finally, we
provide a numerical example to illustrate the merits of the introduced bounds.
