Solving Smooth Min-Min and Min-Max Problems by Mixed Oracle Algorithms

In this paper, we consider two types of problems that have some similarity in their structure, namely, min-min and min-max saddle-point problems. Our approach is based on considering the outer minimization problem as a with inexact oracle. This oracle calculated via solution inner problem, which either or maximization problem. main assumptions are smooth available mixed: it only possible to evaluate gradient w.r.t. block variables corresponds whereas for zeroth-order available. To solve use accelerated gradient-free method variant Vaydya's cutting-plane method. As result, propose framework leads non-asymptotic complexity bounds both Moreover, estimate separately number first- calls sufficient reach any desired accuracy.