$$
\begin{array}{l} \mathbb {E} \left[ \tilde {R} _ {\mathrm {C D}} (g) \right] - R (g) \\ = \int_ {\mathcal {D} _ {n} \in \mathcal {D} _ {n} ^ {-} (g)} (\widetilde {R} _ {\mathrm {C D}} (g) - \widehat {R} _ {\mathrm {C D}} (g)) p (\mathcal {D} _ {n}) \mathrm {d} \mathcal {D} _ {n} \\ \leq \sup  _ {\mathcal {D} _ {n} \in \mathfrak {D} _ {n} ^ {-} (g)} (\widetilde {R} _ {\mathrm {C D}} (g) - \widehat {R} _ {\mathrm {C D}} (g)) \int_ {\mathcal {D} _ {n} \in \mathfrak {D} _ {n} ^ {-} (g)} p (\mathcal {D} _ {n})   \mathrm {d} \mathcal {D} _ {n} \\ = \sup  _ {\mathcal {D} _ {n} \in \mathfrak {D} _ {n} ^ {-} (g)} (\widetilde {R} _ {\mathrm {C D}} (g) - \widehat {R} _ {\mathrm {C D}} (g)) \mathbb {P} \left(\mathfrak {D} _ {n} ^ {-} (g)\right) \\ = \sup  _ {\mathcal {D} _ {n} \in \mathfrak {D} _ {n} ^ {-} (g)} \left(f (\widehat {A} (g)) + f (\widehat {B} (g)) + f (\widehat {C} (g)) + f (\widehat {D} (g)) \right. \\ - \widehat {A} (g) - \widehat {B} (g) - \widehat {C} (g) - \widehat {D} (g)) \mathbb {P} \left(\mathfrak {D} _ {n} ^ {-} (g)\right) \\ \leq \sup  _ {\mathcal {D} _ {n} \in \mathfrak {D} _ {n} ^ {-} (g)} \left(L _ {f} | \widehat {A} (g) | + L _ {f} | \widehat {B} (g) | + L _ {f} | \widehat {C} (g) | + L _ {f} | \widehat {D} (g) |\right. \\ + | \widehat {A} (g) | + | \widehat {B} (g) | + | \widehat {C} (g) | + | \widehat {D} (g) |) \mathbb {P} \left(\mathfrak {D} _ {n} ^ {-} (g) \right. \\ = \sup  _ {\mathcal {D} _ {n} \in \mathfrak {D} _ {n} ^ {-} (g)} \frac {L _ {f} + 1}{2 n} \left(\left| \sum_ {i = 1} ^ {n} \left(\pi_ {+} - c _ {i}\right) \ell \left(g \left(\boldsymbol {x} _ {i}\right), + 1\right) \right| + \left| \sum_ {i = 1} ^ {n} \left(\pi_ {-} - c _ {i}\right) \ell \left(g \left(\boldsymbol {x} _ {i} ^ {\prime}\right), - 1\right) \right| \right. \\ + \left| \sum_ {i = 1} ^ {n} \left(\pi_ {+} + c _ {i}\right) \ell \left(g \left(\boldsymbol {x} _ {i} ^ {\prime}\right), + 1\right) \right| + \left| \sum_ {i = 1} ^ {n} \left(\pi_ {-} + c _ {i}\right) \ell \left(g \left(\boldsymbol {x} _ {i}\right), - 1\right) \right|) \mathbb {P} \left(\mathfrak {D} _ {n} ^ {-} (g)\right) \\ \leq \sup  _ {\mathcal {D} _ {n} \in \mathfrak {D} _ {n} ^ {-} (g)} \frac {L _ {f} + 1}{2 n} \left(\sum_ {i = 1} ^ {n} | (\pi_ {+} - c _ {i}) \ell (g (\boldsymbol {x} _ {i}), + 1) | + \sum_ {i = 1} ^ {n} | (\pi_ {-} - c _ {i}) \ell (g (\boldsymbol {x} _ {i} ^ {\prime}), - 1) |\right. \\ + \sum_ {i = 1} ^ {n} | (\pi_ {+} + c _ {i}) \ell (g \left(\boldsymbol {x} _ {i} ^ {\prime}\right), + 1) | + \sum_ {i = 1} ^ {n} | (\pi_ {-} + c _ {i}) \ell (g \left(\boldsymbol {x} _ {i}\right), - 1) |) \mathbb {P} \left(\mathfrak {D} _ {n} ^ {-} (g)\right) \\ = \sup  _ {\mathcal {D} _ {n} \in \mathfrak {D} _ {n} ^ {-} (g)} \frac {L _ {f} + 1}{2 n} \sum_ {i = 1} ^ {n} \left(\left| \left(\pi_ {+} - c _ {i}\right) \ell \left(g \left(\boldsymbol {x} _ {i}\right), + 1\right) \right| + \left| \left(\pi_ {-} - c _ {i}\right) \ell \left(g \left(\boldsymbol {x} _ {i} ^ {\prime}\right), - 1\right) \right| \right. \\ + \left|\left(\pi_ {+} + c _ {i}\right) \ell \left(g \left(\boldsymbol {x} _ {i} ^ {\prime}\right), + 1\right)\right| + \left|\left(\pi_ {-} + c _ {i}\right) \ell \left(g \left(\boldsymbol {x} _ {i}\right), - 1\right)\right|\left. \right) \mathbb {P} \left(\mathfrak {D} _ {n} ^ {-} (g)\right) \\ \leq \sup  _ {\mathcal {D} _ {n} \in \mathfrak {D} _ {n} ^ {-} (g)} \frac {(L _ {f} + 1) C _ {\ell}}{2 n} \sum_ {i = 1} ^ {n} (| \pi_ {+} - c _ {i} | + | \pi_ {-} - c _ {i} | + | \pi_ {+} + c _ {i} | + | \pi_ {-} + c _ {i} |) \mathbb {P} (\mathfrak {D} _ {n} ^ {-} (g)). \\ \end{array}
$$