Table 1.

Algorithm for reinforcement learning trees

Draw M bootstrap samples from D. For the m-th bootstrap sample, where m ∈ {1, …, M}, fit one RLT model f̂m, using the following rules: At an internal node A, fit an embedded model ${\widehat{f}}_A^{\ast }$ to the training data in A, restricted to the set of variables $\{1,2,\dots ,p\}\backslash {\mathcal{P}}_A^d$, i.e. $\mathcal{P}\backslash {\mathcal{P}}_A^d$, where ${\mathcal{P}}_A^d$ is the set of muted variables at the current node A. Details are given in Section 2.4. Using ${\widehat{f}}_A^{\ast }$, calculate the variable importance measure ${\widehat{VI}}_A(j)$ for each variable X(j), where j ∈ . Details are given in Section 2.5. Split node A into two daughter nodes using the variable(s) with the highest variable importance measure (Section 2.7). Update the set of muted variables for the two daughter nodes by adding the variables with the lowest variable importance measures at the current node. Details are given in Section 2.6. Apply a)–d) on each daughter node until node sample size is smaller than a pre-specified value nmin. Average M trees to get a final model $\widehat{f}=M^{-1}{\sum }_{m=1}^M{\widehat{f}}_m$. For classification, $\widehat{f}=I\left(0.5<M^{-1}{\sum }_{m=1}^M{\widehat{f}}_m\right)$.