To facilitate the following derivation, we rewrite the objective J E+I(E+I) JE(E): 438 J E+I(E+I) JE(E) = E E+ I h 1X

A.1 Full derivation425 We present the complete derivation of the objective function in each subproblem defined in Section426 3.2. For brevity, let rt =(1+)rEt +rIt and V EE (st)= Vt. Under this assumption, E serves as 0 (see above). This451 enables updating E+I using the local approximation. We leave relaxing this assumption as future452 work.453