$$
\begin{array}{l} \left\{q = \frac {1}{d} \operatorname {T r} \left[ \left((\lambda + \hat {V}) \mathbb {I} _ {d} + \hat {V} _ {+} \boldsymbol {\Sigma} _ {+} + \hat {V} _ {-} \boldsymbol {\Sigma} _ {-}\right) ^ {- 2} \left(\hat {q} \mathbb {I} _ {d} + \hat {q} _ {+} \boldsymbol {\Sigma} _ {+} + \hat {q} _ {-} \boldsymbol {\Sigma} _ {-} + \hat {m} ^ {2} d \boldsymbol {\mu} \boldsymbol {\mu} ^ {\top}\right) \right] \right. \\ \left| m = \hat {m} \operatorname {T r} \left[ \left(\left(\lambda + \hat {V}\right) \mathbb {I} _ {d} + \hat {V} _ {+} \boldsymbol {\Sigma} _ {+} + \hat {V} _ {-} \boldsymbol {\Sigma} _ {-}\right) ^ {- 1} \boldsymbol {\mu} \boldsymbol {\mu} ^ {\top} \right. \right. \\ \left. \left. V = \frac {1}{d} \operatorname {T r} \left[ \left(\lambda + \hat {V}\right) \mathbb {I} _ {d} + \hat {V} _ {+} \boldsymbol {\Sigma} _ {+} + \hat {V} _ {-} \boldsymbol {\Sigma} _ {-}\right) ^ {- 1} \right] \right. \\ q _ {\pm} = \frac {1}{d} \operatorname {T r} \left[ \left((\lambda + \hat {V}) \mathbb {I} _ {d} + \hat {V} _ {+} \boldsymbol {\Sigma} _ {+} + \hat {V} _ {-} \boldsymbol {\Sigma} _ {-}\right) ^ {- 1} \boldsymbol {\Sigma} _ {\pm} \left((\lambda + \hat {V}) \mathbb {I} _ {d} + \hat {V} _ {+} \boldsymbol {\Sigma} _ {+} + \hat {V} _ {-} \boldsymbol {\Sigma} _ {-}\right) ^ {- 1} \left(\hat {q} \mathbb {I} _ {d} + \hat {q} _ {+} \boldsymbol {\Sigma} _ {+} + \hat {q} _ {-} \boldsymbol {\Sigma} _ {-} + \hat {m} ^ {2} d \boldsymbol {\mu} \boldsymbol {\mu} ^ {\top}\right) \right] \\ \left. \left\lfloor V _ {\pm} = \frac {1}{d} \operatorname {T r} \left[ \boldsymbol {\Sigma} _ {\pm} \left(\left(\lambda + \hat {V}\right) \mathbb {I} _ {d} + \hat {V} _ {+} \boldsymbol {\Sigma} _ {+} + \hat {V} _ {-} \boldsymbol {\Sigma} _ {-}\right) ^ {- 1} \right] \right. \right. \\ \left\{\hat {m} = \alpha \left[ \rho \frac {1}{V _ {+}} \mathbb {E} _ {\xi , \eta} \left(\operatorname {p r o x} _ {y} ^ {+} - \sqrt {q _ {+}} \eta - m\right) - (1 - \rho) \frac {1}{V _ {-}} \mathbb {E} _ {\xi , \eta} \left(\operatorname {p r o x} _ {y} ^ {-} - \sqrt {q _ {-}} \eta + m\right) \right] \right. \\ \left| \hat {q} = \frac {\alpha}{V ^ {2} \Delta} \left[ \rho \mathbb {E} _ {\xi , \eta} \left(\operatorname {p r o x} _ {x} ^ {+} - \sqrt {q} \sqrt {\Delta} \xi\right) ^ {2} + (1 - \rho) \mathbb {E} _ {\xi , \eta} \left(\operatorname {p r o x} _ {x} ^ {-} - \sqrt {q} \sqrt {\Delta} \xi\right) ^ {2} \right] \right. \\ \left| \hat {V} = - \alpha \left[ \rho \mathbb {E} _ {\xi , \eta} \left[ \frac {\xi (\operatorname {p r o x} _ {x} ^ {+} - \sqrt {q} \sqrt {\Delta} \xi)}{\sqrt {q} \sqrt {\Delta} V} - \sigma (\sqrt {1 - \Delta} \operatorname {p r o x} _ {y} ^ {+} + \operatorname {p r o x} _ {x} ^ {+}) ^ {2} \right] \right. \right. \\ \left. \quad + (1 - \rho) \mathbb {E} _ {\xi , \eta} \left[ \frac {\xi \left(\operatorname {p r o x} _ {x} ^ {-} - \sqrt {q} \sqrt {\Delta} \xi\right)}{\sqrt {q} \sqrt {\Delta} V} - \sigma \left(\sqrt {1 - \Delta} \operatorname {p r o x} _ {y} ^ {-} + \operatorname {p r o x} _ {x} ^ {-}\right) ^ {2} \right] \right] \tag {70} \\ \left\{ \begin{array}{l} \hat {q} _ {+} = \alpha \rho \frac {1}{V _ {+} ^ {2}} \mathbb {E} _ {\xi , \eta} \left(\operatorname {p r o x} _ {y} ^ {+} - \sqrt {q _ {+}} \eta - m\right) ^ {2} \\ \hat {q} _ {-} = \alpha (1 - \rho) \frac {1}{V ^ {2}} \mathbb {E} _ {\xi , \eta} \left(\operatorname {p r o x} _ {y} ^ {-} - \sqrt {q _ {-}} \eta - m\right) ^ {2} \end{array} \right. \\ \left| \hat {V} _ {+} = - \alpha \rho \frac {1}{\sqrt {q _ {+}} V _ {+}} \mathbb {E} _ {\xi , \eta} \left(\operatorname {p r o x} _ {y} ^ {+} - \sqrt {q _ {+}} \eta - m\right) \eta \right. \\ \left\{\hat {V} _ {-} = - \alpha (1 - \rho) \frac {1}{\sqrt {q _ {-}} V _ {-}} \mathbb {E} _ {\xi , \eta} \left(\operatorname {p r o x} _ {y} ^ {-} - \sqrt {q _ {-}} \eta + m\right) \eta \right. \\ \end{array}
$$