Algorithm 1 Cost-based MILP algorithms for the DRO task offloading problem.

Input: the convex probability distributional set ${\mathcal{M}}^{\xi }$, stochastic sample space ${\mathcal{F}}^{\xi }$, trade-off coefficient $\lambda$, confidence level $\alpha$, ambiguous set parameters ${\gamma }_1$ and ${\gamma }_2$; Output: offload decision X, optimal cost value to satisfy distribution robustness; Solve the MILP formulation SDP problem with a confidence level of $\alpha$, to obtain the optimal values of the continuous variables X and the optimal cost value; for i from 0 to $N-1$ do    Sort($\mathcal{N}$)    $[opt,X]=max\left(X_i\right)$    $[x{1}_{ij},x{2}_{ij}]=max2\left(X\right)$    if $SDP(X^{\prime },x_{i,j1}^{\prime }=1)\le SDP(X^{\prime },x_{i,j2}^{\prime }=1)$ then      $x_{i,j1}^{\prime }=1$      $min\_cost\left[i\right]=SDP(X^{\prime },X_{i,j1}^{\prime }=1)$    else      $x_{i,j2}^{\prime }=1$      $min\_cost\left[i\right]=SDP(X^{\prime },X_{i,j2}^{\prime }=1)$    end if end for if $min\_cost[N-1]!=NaN$ then    $return{X}^{\prime },min\_cost[N-1]$ end if