1. The proposed algorithm DMLCBO is based on double momentum technique. In previous works, e.g., SUSTAIN[1] and MRBO[2], double momentum technique improves the convergence rate to $\mathcal{\widetilde O}(\epsilon^{-3})$ while proposed algorithm only achieves the $\mathcal{\widetilde O}(\epsilon^{-4})$. The authors are encouraged to discuss the reason why DMLCBO does not achieve it and the theoretical technique difference between DMLCBO and above mentioned works.
2. In the experimental part, the author only shows the results of DMLCBO in early time, it will be more informative to provide results in the later steps.
3. In Table 3, DMLCBO exhibits higher variance compared with other baselines in MNIST datasets, the authors are encouraged to discuss more experimental details about it and explain the behind reason.
[1] A Near-Optimal Algorithm for Stochastic Bilevel Optimization via Double-Momentum
[2] Provably Faster Algorithms for Bilevel Optimization
1. The proposed algorithm DMLCBO is based on double momentum technique. In previous works, e.g., SUSTAIN[1] and MRBO[2], double momentum technique improves the convergence rate to $\mathcal{\widetilde O}(\epsilon^{-3})$ while proposed algorithm only achieves the $\mathcal{\widetilde O}(\epsilon^{-4})$. The authors are encouraged to discuss the reason why DMLCBO does not achieve it and the theoretical technique difference between DMLCBO and above mentioned works.