&\\
        &+ \sum_{\tau=1}^T {\mathcal{O}}(\frac{1}{\sqrt{n_\tau}}).
    \end{aligned}$$

The intuition behind Lemma \[lem:rademacher-tasks\] is that the upper bound on the Rademacher complexity increases when the tasks are dissimilar. The dissimilarity between two subsequent tasks is measured through ${\mbox{${\mbox{$\mathbf{\tilde{y}}$}}$}}_\tau^T (k_t({\mbox{${\mbox{$\mathbf{X}$}}$}}_\tau , {\mbox{${\mbox{$\mathbf{X}$}}$}}_\tau) +
        \lambda^2 {\mbox{${\mbox{$\mathbf{I}$}}$}})^{-1}  {\mbox{${\mbox{$\mathbf{\tilde{y}}$}}$}}_\tau$. The knowledge from the previous tasks is implicitly encoded in the kernel $k_\tau$, which is based on the feature map $\phi_\tau$. This feature map encodes the acquired knowledge. As an edge case, if two successive tasks are identical, the residual ${\mbox{${\mbox{$\mathbf{\tilde{y}}$}}$}}_\tau = {\mbox{${\mbox{$\mathbf{y}$}}$}}_\tau -
{\mbox{${\mbox{$\mathbf{y}$}}$}}_{\tau - 1 \rightarrow \tau} = 0$, therefore, the upper bound on the Rademacher complexity does not increase.

#### Implications for Curriculum Learning

We also observe that the upper bound depends on the task ordering, which may provide a theoretical explanation on the importance of learning with a curriculum [@Bengio2009curriculum]. In the following, we present an edge case which provided an intuition on how the bound captures the importance of the order. Consider two dissimilar tasks ${\mbox{$\mathcal{T}$}}_1$ and ${\mbox{$\mathcal{T}$}}_2$. A sequence of tasks alternating between ${\mbox{$\mathcal{T}$}}_1$ and ${\mbox{$\mathcal{T}$}}_2$ will lead to a large upper bound, as explained in the first paragraph. While, a sequence of tasks concatenating two sequences of ${\mbox{$\mathcal{T}$}}_1$ then ${\mbox{$\mathcal{T}$}}_2$ will 