Then momentum acceleration is also introduced into our dual accelerating update step.

Then momentum acceleration is also introduced into our dual accelerating update step.

Many zeroth-order (ZO) optimization algorithms have been developed to solve nonconvex minimax problems in machine learning and computer vision areas.

As training data become larger, distributed training has been broadly adopted in machine learning tasks.

We thank the reviewers for their careful consideration and their feedback. We provide our responses below. 's improved robustness was obtained over the

An important question arises regarding whether there is a fundamental trade-off between reproducibility and convergence speed in algorithms.

Sharma et al. (2022) provide Y ang et al. (2022a) integrate Local SGDA with stochastic gradient estimators to eliminate the More recently, Zhang et al. (2023) adopt compressed momentum methods with Local SGD to increase the communication efficiency of the algorithm. For centralized nonconvex minimax problems, Y ang et al. (2022b) show that, even in deterministic settings, GDA-based methods necessitate the timescale separation of the stepsizes for primal and dual updates.