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Min MaxOptimizationDeepLearning
%2524+oracle+complexity+to+find+an+%2524varepsilon%2524-stationary+point.+Some+works+indicate+that+this+complexity+can+be+improved+to+%2524mathcal%7bO%7d(varepsilon%5e%7b-3%7d)%2524+when+the+loss+gradient+is+Lipschitz+continuous.+The+question+of+achieving+enhanced+convergence+rates+under+distinct+conditions%252C+remains+unresolved.+In+this+work%252C+we+address+this+question+for+optimization+problems+that+are+nonconvex+in+the+minimization+variable+and+strongly+concave+or+Polyak-Lojasiewicz+(PL)+in+the+maximization+variable.+We+introduce+novel+bias-corrected+momentum+algorithms+utilizing+efficient+Hessian-vector+products.+We+establish+convergence+conditions+and+demonstrate+a+lower+iteration+complexity+of+%2524mathcal%7bO%7d(varepsilon%5e%7b-3%7d)%2524+for+the+proposed+algorithms.+The+effectiveness+of+the+method+is+validated+through+applications+to+robust+logistic+regression+using+real-world+datasets.&cdnurl=https%3a%2f%2fth.bing.com%2fth%2fid%2fR.8ba1e6c6e2e22ff9de40fc53dc37afc6%3frik%3dwbeIGBYX7WNW6w%26pid%3dImgRaw%26r%3d0&exph=630&expw=1200&q=Min+Max+Optimization+Deep+Learning&FORM=IRPRST&ck=3FCC1F94B47E372ED723B76AD487ECDF&selectedIndex=15&itb=0)
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