0cddb777d3441326544e21b67f41bdc8-Supplemental-Conference.pdf

In this section, we prove the Theorem 2.1, which states a problem P and its' orthogonal transformed problem Q(P) = {{Qxi}Ni=1,f}have identical optimal solutions if Qis orthogonal matrix: QQT = QTQ = I. As we mentioned in Section 2.2, reward R is a function of a1:T (solution sequences), ||xi xj||i,j {1,...N} (relative distances) and f (nodes features). And Let R (P)is optimal value of problem P: i.e. Then, the remaining proof is to show Q(P)has an identical solution set with P. Let optimal solution set Π (P) = {πi(P)}Mi=1, where πi(P)indicates optimal solution of P and M is the number of heterogeneous optimal solution. Conversely, For any πi(P) Π (P), they have sample optimal value with Q(P): R(πi(P);P) = R (P) = R (Q(P)) Thus, πi(P) Π (Q(P)).