1. The title is misleading and the authors might overclaim their contribution. Indeed, the stochastic problem in Eq.(1) is a special instance of nonconvex-concave minimax problems and equivalent to nonconvex compositional optimization problem in Eq.(2). Solving such problem is easier than the general case consider in [23, 34]; see also (Rafique, Arxiv 1810.02060) and (Thekumparampil, NeurIPS'19). In addition, the KKT points and approximate KKT points are also defined based on such special structure. 2. The literature review is not complete. The authors mainly focus on the algorithms for stochastic compositional optimization instead of stochastic nonconvex-concave minimax optimization. 3. The algorithm is not single-loop in general. To be more specific, Algorithm 1 needs to solve Eq.(9) at each loop. This is also a nonsmooth strongly convex problem in general and the solution does not have the closed form. To this end, what is the advantage of Algorithm 1 over prox-linear algorithms in nonsmooth case? 4. Given the current stochastic problem in Eq.(1), I believe that the prox-linear subproblem can be reformulated using the conjugate function and becomes the same as the subproblem in Algorithm 1. That is to say, we can simply improve prox-linear algorithms for solving stochastic problem in Eq.(1). This makes the motivation of Algorithm 1 unclear. 5. The proof techniques heavily depend on the biased hybrid estimators introduced in [29]. The current paper does not convince me that such extension is nontrivial and has sufficient technical novelty.
4. Given the current stochastic problem in Eq.(1), I believe that the prox-linear subproblem can be reformulated using the conjugate function and becomes the same as the subproblem in Algorithm 1. That is to say, we can simply improve prox-linear algorithms for solving stochastic problem in Eq.(1). This makes the motivation of Algorithm 1 unclear.