T$, $i \in \{1,\ldots,\ell\}$, the local prediction function at leaf $L_i$ is a linear predictor $\bx \mapsto \inner{f_i,\bx}$, which we parametrize by the vector $f_i$, under the constraint $f_{i} \in B$; we will consider the constrained classes of the form $ B := \{ \norm{f} \leq W\} \subset \mbr^d$, where $\norm{\cdot}$ is some norm in $\mathbb{R}^{d}$, and track the influence of norm constraints (for some specific choice of norm) on the complexity terms.

Using the aforementioned notation, we can describe class of regression decision trees as follows: $$\begin{aligned}
\label{func_class001}
\mathcal{F} := \{f : f = \paren{ T, (i_{s},t_{s})_{s \in T^{\circ}},(f_{k})_{k \in \partial T}}, T \in \mathcal{T}_{\ell},  \paren{i_s,t_s} \in [D]\times \mathbb{R}, f_{k} \in B \}.\end{aligned}$$ The main aim of the next section is to obtain error bounds for statistical performance of the functional class by means of the deviation of its generalization error. The main technical tool is the concept of Rademacher complexity.

Theoretical analysis  {#sec:theor_analysis}
=====================

Preliminaries and aim.
----------------------

In the following analysis, we obtain high probability upper bounds on the deviation of the *statistical risk* $L(f) = E_{P_{X,Y}}[\ell(f(\bx),y)]$ of the model $f \in\mathcal{F}$ from *empirical risk* $\hat{L}_{n}(f) = \frac{1}{n}\sum_{i=1}^{n}\ell(f({\bx_{i}}),y_{i})$ uniformly over the model class $\mathcal{F}$. We define the 